- About
- Admissions
- Study at AUS
- Prospective Students
- Bachelor's Degrees
- Master's Degrees
- Doctoral Degrees
- Admission Publications
- International Students
- Contact Admissions
- Grants and Scholarships
- Sponsorship Liaison Services
- Testing Center
- New Student Guide
- File Completion
- New Student Orientation
- Payment Guide
- Executive Education
- Students with Disabilities

- Academics
- Life at AUS
- Research and Graduate Studies
- Contact Us
- Apply Now
- .

## Profile

## College / Department

## Teaching areas

Linear Algebra, Differential Equation, Discrete Math., Calculus, Business Math., Geometry, Abstract Algebra, Number Theory, Graph Theory and Math. for Architects . (More details are available on my personal web page www.ayman-badawi.com ).

## Research areas

Commutative Ring Theory. Most of my work is devoted to multiplicative ideal theory (school of Kaplansky and Gilmer). For example, I introduced the following concepts: phi-Commutative Rings , a class of commutative rings contains the class of integral domains. I introduced the concepts of absorbing ideals, Total graph of a commutative ring, annihilator graph of a commutative ring, dot-product graph of a commutative rings. Other interests include regular rings and their generalizations.

## Education

PhD, Ring Theory: Pi-regular Rings., University of North Texas, United States, 1993

MS, Master Degree In Mathematics, Tennessee Tech. University, United States, 1988

Bachelor, Double Major: Mathematics And Computer Science, Tennessee Tech. University, United States, 1986

## Professional experience

Associate Professor And Then Professor, American University of Sharjah, Sharjah, United Arab Emirates, 2003 - Present

Assistant Professor And Then Associate Professor, Birzeit University, Birzeit, Palestine, 1997 - 2003

Visiting Assistant Professor, Emory and Henry College, Virginia, United States, 1994 - 1996

## Memberships

American Math. Society, AMS, International, August 1994

## Contact

+971 6 515 2573

# Dr. Ayman Badawi

Professor

PhD, University of North Texas, United States

Ayman Badawi has taught in mathematics departments for more than 25 years at institutions such as Emory & Henry College, Virginia, USA; the University of Tennessee-Knoxville, USA; and Birzeit University, West Bank, Palestine. His area of research is in commutative algebra and his teaching interests are linear algebra, abstract algebra, number theory, discrete math, calculus, differential equations, math for architects, geometry, graph theory and business math.

## Publications

Ayman Badawi. Absorbing Ideals in Commutative Rings: A Survey, 20 June 2023

Ayman Badawi, Abdelhaq El Khalfi And Najib Madou. On (m, n)‑absorbing prime ideals and (m, n)‑absorbing ideals of commutative rings, São Paulo Journal Of Mathematical Sciences, February 2023

Ayman Badawi And Yasmine El-ashi. Graph of Linear Transformations over R, Springer Proceedings In Mathematics & Statistics, December 2022

Ayman Badawi And Ece Celikel. On Weakly 1-Absorbing Primary Ideals of Commutative Rings, Algebra Colloquium, 22 July (3rd Quarter/Summer) 2022

Ayman Badawi And David Anderson. The n-zero-divisor graph of a commutative semigroup, Communications In Algebra, 16 April (2nd Quarter/Spring) 2022

Ayman Badawi And Jim Coykendall. Rings, Monoids and Module Theory (AUS-ICMS20, Proceedings of the special session on rings, monoids and module theory organized by Ayman Badawi), 14 March 2022

Ayman Badawi, David Anderson, T Asir And T. Tamizh Chelvam. Graphs from Rings, 12 November 2021

Ayman Badawi And Rosi Rissner. Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory, Open Mathematics, 30 December 2020

Ayman Badawi And Brahim Fahid. On weakly 2-absorbing δ-primary ideals of commutative rings, Georgian Mathematical Journal, 1 December 2020

Mohammad Abdulla And Ayman Badawi. ON DOT PRODUCT GRAPH OF A COMMUTATIVE RING II, International Electronic Journal Of Algebra, 2 September 2020

David Anderson And Ayman Badawi. On n-semiprimary ideals andn-pseudo valuation domains, Communications In Algebra, 14 August 2020

Ayman Badawi And Ece Çelikel. On 1-absorbing primary ideals of commutative rings, Journal Of Algebra And Its Applications, 1 June 2020

Ayman Badawi, Mohammed Issoual And Najib Mahdou. On n-absorbing ideals and (m,n)-closed ideals in trivial ring extensions of commutative rings, Journal Of Algebra And Its Applications, 23 July (3rd Quarter/Summer) 2019

Ayman Badawi And Jim Coykendall. Advances in commutative algebra, 1 May 2019

Ayman Badawi, Deniz Sonmez And Gursel Yesilot. On Weakly δ-Semiprimary Ideals of Commutative Rings, Algebra Colloquium, 1 September 2018

Ayman Badawi, David Anderdon And Brahim Fahid. Weakly (m,n)-closed ideals and (m,n)-von Neumann regular rings, Journal Of The Korean Mathematical Society, 1 September 2018

Ayman Badawi, Reda Alhajj And Jon Rokne. Matrix Algebra, Basics of, 12 June 2018

Ayman Badawi, Mohammad Vedadi, Siamak Yassemi And Ahmad Darani. Homological and Combinatorial Methods in Algebra, April (2nd Quarter/Spring) 2018

Ayman Badawi, Marco Fontana, Sophie Frisch, Sarah Glaz And Francesca Tartarone. N-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A survey, November 2017

Ayman Badawi, David Anderson, Manfred Droste, László Fuchs, Brendan Goldsmith And Lutz Strüngmann. The Zero-Divisor Graph of a Commutative Semigroup: A Survey,, July (3rd Quarter/Summer) 2017

Ayman Badawi, K. Prasad, K. Srinivas, H. Panackal, B. Satyaanarayana, K. Neuerburg, G. Booth, B. Davvas, M. Farag And S. Juglal. Nearrings, NearFields, and Related Topics, February 2017

Ayman Badawi, K. Prasad And K. Prasad. Recent results on annihilator graph of a commutative ring: A survey, 23 February 2017

David Anderson And Ayman Badawi. On (m, n)-closed ideals of commutative rings, Journal Of Algebra And Its Applications, 1 January (1st Quarter/Winter) 2017

Ayman Badawi. On weakly semiprime ideals of commutative rings, Beitraege Zur Algebra Und Geometrie, 1 September 2016

Ayman Badawi, Ünsal Tekir, Emel Aslankarayiğit Uğurlu, Gülşen Ulucak And Ece Yetkin Çelikel. Generalizations of 2-absorbing primary ideals of commutative rings, Turkish Journal Of Mathematics, 1 January (1st Quarter/Winter) 2016

Ayman Badawi. On the Dot Product Graph of a Commutative Ring, Communications In Algebra, 1 January (1st Quarter/Winter) 2015

Ayman Badawi, Unsal Tekir And Ece Yetkin. On weakly 2-absorbing primary ideals of commutative rings, Journal Of The Korean Mathematical Society, 1 January (1st Quarter/Winter) 2015

Ayman Badawi, M. Fontana And M. Fontana. On the Total Graph of a Ring and Its RelatedGraphs: A Survey, September 2014

Ayman Badawi, Unsal Tekir And Ece Yetkin. On 2-absorbing primary ideals in commutative rings, Bulletin Of The Korean Mathematical Society, 1 January (1st Quarter/Winter) 2014

Ayman Badawi. On the annihilator graph of a commutative ring, Communications In Algebra, 1 January (1st Quarter/Winter) 2014

Ayman Badawi And Ahmad Darani. On weakly 2-absorbing ideals of commutative rings, Houston Journal Of Mathematics, 19 August 2013

David Anderson And Ayman Badawi. The generalized total graph of a commutative ring, Journal Of Algebra And Its Applications, 1 August 2013

David Anderson And Ayman Badawi. Von neumann regular and related elements in commutative rings, Algebra Colloquium, 1 December 2012

David Anderson And Ayman Badawi. On the total graph of a commutative ring without the zero element, Journal Of Algebra And Its Applications, 1 August 2012

Ayman Badawi, J. Abuhlail, S. Kabbaj, A. Jaballah, A. Laradji And R. Wisbauer. Selected Papers from the Algebra Sessions at the First International Conference on Mathematics and Statistics (AUS-ICMS'10),, Arabian Journal Of Mathematics, April (2nd Quarter/Spring) 2012

Ayman Badawi, J. Abuhlail, S. Kabbaj, A. Jaballah, A. Laradji And R. Wisbauer. Mathematics - Part One (pp. 919-1070) First International Conference on Mathematics and Statistics (AUS-ICMS'10); Part Two (pp. 1071-1169): Regular Articles, Arabian Journal For Science And Engineering, June 2011

David Anderson And Ayman Badawi. On n-absorbing ideals of commutative rings, Communications In Algebra, 1 May 2011

Ayman Badawi, David Anderson, David Dobbs, Jay Shapiro, Marco Fontana, Salah-eddine Kabbaj, Bruce Olberding And Irena Swanson. Divisibility properties in ultrapowers of commutative rings, September 2009

Ayman Badawi, Marco Fontana, Salah-eddine Kabbaj, Bruce Olberding And Irena Swanson. On rings with divided nil ideal: a survey, 1 September 2009

David Anderson And Ayman Badawi. The total graph of a commutative ring, Journal Of Algebra, 1 October (4th Quarter/Autumn) 2008

David Anderson And Ayman Badawi. On the zero-divisor graph of a ring, Communications In Algebra, 1 August 2008

Ayman Badawi And Ali Jaballah. Some finiteness conditions on the set of overrings of a φ-ring, Houston Journal Of Mathematics, 25 July (3rd Quarter/Summer) 2008

Ayman Badawi. On 2-absorbing ideals of commutative rings, Bulletin Of The Australian Mathematical Society, 1 June 2007

Ayman Badawi. On pseudo-almost valuation domains, Communications In Algebra, 1 April (2nd Quarter/Spring) 2007

Ayman Badawi, Pat Goeters And Overtoun Jenda. A Counter example for a question on pseudo-valuation rings, 2 September 2006

Ayman Badawi And David Dobbs. Strong ring extensions and Φ-pseudo-valuation rings, Houston Journal Of Mathematics, 17 August 2006

Ayman Badawi And Thomas Lucas. On Φ-Mori rings, Houston Journal Of Mathematics, 15 May 2006

Ayman Badawi. Focus on Commutative Rings Research, 5 May 2006

David Anderson And Ayman Badawi. On φ-Dedekind rings and φ-Krull rings, Houston Journal Of Mathematics, 1 December 2005

Ayman Badawi. Factoring nonnil ideals into prime and invertible ideals, Bulletin Of The London Mathematical Society, 1 October (4th Quarter/Autumn) 2005

Ayman Badawi, Lucas Thomas And Scott Chapman. Rings with prime nilradical, 8 September 2005

Ayman Badawi. A characterization of valuation domains via m-canonical ideals, Communications In Algebra, 1 December 2004

Ayman Badawi. Abstract Algebra Manual: Problems and Solutions, April (2nd Quarter/Spring) 2004

David Anderson And Ayman Badawi. On φ-Prüfer rings and φ-Bezout rings, Houston Journal Of Mathematics, 1 January (1st Quarter/Winter) 2004

Ayman Badawi. On Nonnil-Noetherian rings, Communications In Algebra, 1 April (2nd Quarter/Spring) 2003

David Anderson And Ayman Badawi. Divisibility conditions in commutative rings with zerodivisors, Communications In Algebra, 1 August 2002

Ayman Badawi, S Elaydi, E Titi, M Saleh, R Abu-saris And Sk Jain. PSEUDO-VALUATION DOMAINS: A SURVEY, 22 May 2002

Ayman Badawi And Evan Houston. Powerful ideals, strongly primary ideals, almost pseudo-valuation domains, and conducive domains, Communications In Algebra, 1 April (2nd Quarter/Spring) 2002

Ayman Badawi, Marco Fontana, Salah-eddine Kabbaj And Sylvia Wiegand. On the complete integral closure of rings that admit a phi-strongly prime ideal, 20 March 2002

Ayman Badawi, Chin And Chen. On rings with near idempotent elements, International J. Of Pure And Applied Math, 3 March 2002

Ayman Badawi. On φ-chained rings and φ-pseudo-valuation rings, Houston Journal Of Mathematics, 1 December 2001

Ayman Badawi, David Dobbs, Daniel Anderson And Ira Papick. Some examples of locally divided rings, June 2001

Ayman Badawi, David Anderson, Daniel Anderson And Ira Papick. Conditions equivalent to seminormality in certain classes of commutative rings, 7 June 2001

Ayman Badawi And David Dobbs. On locally divided rings and going-down rings, Communications In Algebra, 1 January (1st Quarter/Winter) 2001

David Anderson And Ayman Badawi. On root closure in commutative rings, Arabian Journal For Science And Engineering, 1 January (1st Quarter/Winter) 2001

Ayman Badawi. On Φ-pseudo-valuation rings II, Houston Journal Of Mathematics, 1 December 2000

David Anderson, Ayman Badawi And David Dobbs. Pseudo-valuation rings, II, Bollettino Della Unione Matematica Italiana B, 1 June 2000

Ayman Badawi. On chained overrings of pseudo-valuation rings, Communications In Algebra, 1 January (1st Quarter/Winter) 2000

Ayman Badawi. Remarks on pseudo-valuation rings, Communications In Algebra, 1 January (1st Quarter/Winter) 2000

Ayman Badawi, David Dobbs, Marco Fontana And Salah-eddine Kabbaj. On φ-pseudo-valuation rings, August 1999

Ayman Badawi. On divided commutative rings, Communications In Algebra, 1 January (1st Quarter/Winter) 1999

Ayman Badawi. On comparability of ideals of commutative rings, Communications In Algebra, 1 January (1st Quarter/Winter) 1998

Ayman Badawi, David Anderson, David Dobbs, Paul-jean Cahen, Marco Fontana, Evan Houston And Salah-eddine Kabbaj. Pseudo-valuation rings, October (4th Quarter/Autumn) 1997

Ayman Badawi. On abelian π-regular rings, Communications In Algebra, 1 January (1st Quarter/Winter) 1997

Ayman Badawi. On domains which have prime ideals that are linearly ordered, Communications In Algebra, 1 January (1st Quarter/Winter) 1995

Ayman Badawi, David Anderson And David Dobbs. A visit to valuation and pseudo-valuation domains, 18 September 1994

Ayman Badawi. On semicommutative ii-regular rings., Communications In Algebra, 1 January (1st Quarter/Winter) 1994

Ayman Badawi. R(N) CONTAINS A DIVISION RING IFF-R DOES, American Mathematical Monthly, 1993

## Conference Presentations

Square difference factor absorbing ideals in commutative rings, International Conference On Semigroups, Operators, And Automata 2024, 23 May 2024

Square difference factor absorbing ideals in a commutative ring, Workshop On Algebra, Combinatorics, And Applications, 20 April 2024

Square difference factor absorbing ideals in a commutative ring, The Southern Regional Algebra Conference-24 (srac24), University Of Houston, Texas, Usa, 24 March 2024

CHARACTERIZING SOME COMMUTATIVE RINGS BY DIVISIBILITY CONDITIONS, Uae-math-day, 2 March 2024

Characterizing some commutative rings by divisibility conditions, International Conference On Semigroups, Algebras, Discrete Structures, And Applications 2024, 16 February 2024

Some amazing numbers, lecture on the occasion of my birthday., Math Dept -seminars, 23-24, 14 February 2024

On n-pseudo valuation rings, The First Sharjah International Conference On Mathematical Sciences, 6 November 2023

Some amazing numbers, International Conference On Special Functions & Applications (icsfa-2023) (xxiind Annual Meeting Of The Society For Special Functions & Their Applications, India) & Symposium On Algebra & Algebraic Combinatorics, 2 November 2023

Recent developments on absorbing ideals of commutative rings, Ams Sectional Meeting, Southern Univer. Of Alabama, 13 October 2023

Some beautiful results on numbers, Clemson Students Math Club, 29 September 2023

Recent developments on absorbing ideals, Math-seminar At Clemson University, 22 September 2023

Recent developments on absorbing ideals of commutative rings, The International Conference On Algebra And Its Applications (icaa) In Honor Of Ayman Badawi, 13 July 2023

The n-pseudo valuation domains, The Southern Regional Algebra Conference (srac), 26 March 2023

On n-pseudo valuation domains (n-PVD), Symposium On "algebra And Number Theory", 20 March 2023

On 1-absorbing primary ideals of commutative rings, Uae-math-day, 4 March 2023

Graphs from rings, The Xxxviii Interuniversity Seminar On Research In The Mathematical Sciences (sidim) At The University Of Puerto Rico At Mayagüez, 20 February 2023

On the beauty of some numbers., Department Seminar, 14 February 2023

Beautiful results in number theory I, International Conference On Number Theory And Graph Theory (icng-2023), Https://conference.manipal.edu/icng-2023/speakers.aspx, 18 January 2023

Remembering Muhammad Zafrullah, International E-conference Of Young Researchers In Algebra And Number Theory-2023, Https://sites.google.com/view/icyrant-2023/home?authuser=0&pli=1, 12 January 2023

A characterization of valuation domains via m-canonical ideals, International Conference On Algebra, Analysis And Applications, Https://conference.manipal.edu/aaamanipal2023/default.aspx, 6 January 2023

Some results on graphs from rings,, Progress In Mathematics Towards Industrial Application (pmtia-2022), Http://ayman-badawi.com/poster-oct28-india.jpg, 28 October 2022

The n-zerodivisor graph of a commutative semigroup, The Seventh Palestinian Conference On Math And Physics, Https://photos.google.com/share/af1qipp_z-e-fqxtzo0fe2-hboh2zimz06sgkbqhxckcq6u-7jnofdckltjnfp74vdtxza?key=dgyymnnhuudjyi13r2t2a2jfx2rmyllkawozq0vn, 29 July 2022

Pi-regular rings and periodic rings, International Conference On Noncommutative Algebra And Its Applications, 10 May 2022

Absorbing ideals in commutative rings, International E-conference On Pure And Applied Mathematical Sciences (icpams-2022), 6 May 2022

The N-zerodivisor graph of a commutative ring, Annual Southern Regional Algebra Conference (srac), Milledgeville, Ga, Usa, 19 March 2022

Amazing Numbers, Department Seminar, 14 February 2022

N-ZERO-DIVISOR GRAPH OF A COMMUTATIVE SEMIGROUP,, International Conference On Graphs, Combinatorics And Optimization, 7 February 2022

ON DOMAINS WHICH HAVE PRIME IDEALS THAT ARE LINEARLY ORDERED,, 5th International Conference On Current Scenario In Pure And Applied Mathematics (iccspam - 2022), 28 January 2022

On 1-absorbing primary ideals of commutative rings, On Recent Advances In Pure & Applied Algebra (rapaa-2021), 28 October 2021

On graphs arises from Number Theory, 27th International Conference Of International Academy Of Physical Sciences (coniaps Xxvii) On Graph Theory And Applications (gta 2021), 27 October 2021

Results on dot product graphs, International Conference On Discrete Mathematics (icdm 2021), 12 October 2021

A characterization of normal subgroups via closed subsets, Icms 2021, 8 October 2021

On n-pseudo valuation domains, Conference On Rings And Polynomials, 20 July 2021

Von Neumann Regular and Related Elements in Commutative Ring, Noncommutative Rings And Their Applications, Vii, 6 July 2021

ON THE INTERPLAY BETWEEN RING THEORY AND GRAPH THEORY,, International Conference On Emerging Trends In Pure And Applied Mathematics, 21 June 2021

On (m, n)-closed ideals of commutative rings, Southern Regional Algebra Conference (srac 2021), 20 March 2021

Some results on annihilator graph of a commutative ring., 11th Conference On Graph Theory And Algebraic Combinatorics,, 4 March 2021

Ramsey number/, Department Seminar, 14 February 2021

Some results on annihilator graph of a commutative ring., International Virtual Conference On Discrete Mathematics 2021, 10 February 2021

1-absorbing primary ideals,, Iccspam-2021, 29 January 2021

Graphs attached to rings and partial order graphs., (rc-mathematics) At The Ugc – Human Resource Development Centre, University Of North Bengal., 14 January 2021

My personal views on Mathematics and Technology,, Iccems 2020, 24 December 2020

Rings and graphs, International Conference On Recent Trends In Applied And Computational Mathematics-icrtacm-2020,, 4 December 2020

On the zero-divisor graph of commutative semigroups, Five Days International E-seminar On Recent Research In Mathematics, 15 September 2020

N-absorbing ideals of commutative rings, Icpam-van 2020,, 4 September 2020

On n-Pseudo valuation domains, Icmase, 10 July 2020

Total graph and trace graph of a ring, 2nd International Conference On Algebra And Discrete Mathematics, 24 June 2020

Ramsey numbers of partial order graphs and implications in ring theory, Recent Trends In Graph Theory,, 29 May 2020

On generalization of valuation domains, International Conference On Analysis, Algebra, Combinatorics And Their Applications,, 20 January 2020

N-absorbing ideals of commutative rings, 8th International Eurasian Conference On Mathematical Sciences, 27 August 2019

Absorbing ideals and their generalization, The Second Algebra Workshop, 18 July 2019

On n-absorbing ideals of commutative rings, International Conference On Mathematics, 3 July 2019

Graphs arises from Number Theory, International Conference On Number Theory And Graph Theory Honoring Prof. Adiga Renowned Mathematician (known For His Work On Ramanjan's Notebook, 27 June 2019

Recent progress: Conjectures on n-absorbing ideals, 6th International Conference On Pure And Applied Math, 12 June 2019

Recent results on absorbing ideals, 3rd International Congress/ Algebra, Number Theory And Applications, 24 April 2019

On N-pseudo valuation domains, Ams Joint Central And Western Sectional Meeting/ Special Session On "factorization And Arithmetic Properties Of Integral Domains And Monoids, 23 March 2019

On n-Pseudo valuation domains, Uae Math Day, 16 March 2019

Magic numbers, 14 February 2019

On annihilator graph of a commutative ring, International Conference On Graph Theory And Its Application, 5 January 2019

On 1-absorbing primary ideals of commutative rings, International Conference On Mathematics (special Session On Ring Theory Group ), 19 December 2018

On n-absorbing ideals and recent progress on some conjectures, International Conference On Algebra, Icacm-2018, 23 November 2018

On n-absorbing ideals of commutative rings, Sixth Palestinian Conference On Modern Trends In Mathematics And Physics Pcmtmp-vi, 5 August 2018

Graphs associated to commutative rings, 5th International Congress On Fundamental And Applied Sciences 2018, 22 June 2018

## Grants and sponsorships

Grant, Faculty research award FRG21, AUS FRG Program, June 2021 - May 2022

Grant, Faculty Research Grant 2020, FRG20 (Short), American University of Sharjah, 1 June 2020 - 10 January 2021

Grant, Faculty Research Grant 2019 (short ), American University of Sharjah, 1 June 2019 - 30 May 2020

Grant, Travel Grant, University of Granada , Spain, 4 October 2014 - 4 October 2014

Grant, Travel Grant ( only housing and meals), University of Tenessee, Knoxville, USA, 11 November 2013 - 11 November 2013

Grant, Reseach-visitor at University of Roma II, Italian Ministry of University and Scientific and Technological Research (MURST), 1 November 2002 - 17 November 2002

Grant, Ashrawi Scholarship, One-month research grant at Vriji University, Amsterdam, Holand, 1997, 1 October 1997 - 21 October 1997

Grant, Pew Fellowhip, Short-Period Research Grant at the university of Kentucky where I visited Prof. Paul Eakin, 10 June 1994 - 10 July 1994

## Awards and Honors

Faculty research award-Short (FRG-21), AUS FRG PROGRAM, Course release, 1 June 2021

Judging Panellist, The Global Undergraduate Awards 2020 Programme, Evaluate undergraduate research projects, 27 September 2020

Faculty research award FRG-20, AUS-FRG PROGRAM, I received a one-course release., 1 June 2020

Judging Panelist, The Global Undergraduate Awards, Evaluate Undergraduate Research Projects in Math, 1 December 2019

FRG-19, Faculty Research Award, AUS, FRG program, One course release, 1 June 2019

Judging Panellist, The Global Undergraduate Award, Evaluate undergraduate research projects in Math., 10 October 2018

Excellence in Research Award for the Academic year 2014-2015, The Dean of College of Arts and Science at AUS., 22 April 2015

Excellence in Teaching, CAS-Teaching-Award: Excellent in teaching for the year 2012-2013, 5 May 2013