Recent Progress on Three Outstanding Conjectures on n-Absorbing Ideals of Commutative Rings

The Department of Mathematics and Statistics of the College of Arts and Sciences invites you to attend a seminar to be conducted by Dr. Ayman Badawi from American University of Sharjah.

Abstract: Let R be a commutative ring with 1 not equal 0. A proper ideal I of R is called a 2-absorbing ideal of R if a, b, c in R and abc in I, then ab in I or ac in I or bc in I . A more general concept than 2-absorbing ideals is the concept of n-absorbing ideals. Let n > = 1 be an integer. A proper ideal I of R is called an n-absorbing ideal of R if a_1, a_2, a_{n+1} in R and a_1a_2 ... a_{n+1} in I, then there are n of the a_i's whose product is in I. The concept of n-absorbing ideals is a generalization of the concept of prime ideals (note that a prime ideal of R is a 1-absorbing ideal of R). In this talk, we will state recent progress on three outstanding conjectures on n-absorbing ideals of commutative rings.

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