On the 2-Absorbing Ideals in Commutative Rings

作者：Payrovi Sh^*; Babaei S

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2013, 36(4): 895-900.

• 2-absorbing ideal

Let R be a commutative ring with identity. In this article, we study a generalization of prime ideal. A proper ideal I of R is called a 2-absorbing ideal if whenever abc is an element of I for a,b,c is an element of R, then ab is an element of I or bc is an element of I or ac is an element of I. It is shown that if I is a 2-absorbing ideal of a Noetherian ring R, then R/I has some ideals J(n), where 1 <= n <= t and t is a positive integer, such that J(n) possesses a prime filtration F-Jn: 0 subset of R(x(1) + I) subset of R(x(1) + I) circle plus R(x(2) + I) subset of ... subset of R(x(1) + I) circle plus ... circle plus R(x(n) + I) = J(n) with Ass(R)(J(n)) = {I:(R) x(i) vertical bar i = 1, ... , n} and vertical bar Ass(R)(J(n))vertical bar = n. Also, a 2-Absorbing Avoidance Theorem is proved.

• 出版日期2013