# On ( m , n )-absorbing ideals of commutative rings

Research paper by **BATOOL ZAREI JALAL ABADI, HOSEIN FAZAELI MOGHIMI**

Indexed on: **01 Jan '17**Published on: **09 Dec '16**Published in: **Proceedings - Mathematical Sciences**

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#### Abstract

Abstract
Let R be a commutative ring with 1 ≠ 0 and U(R) be the set of all unit elements of R. Let m, n be positive integers such that m > n. In this article, we study a generalization of n-absorbing ideals. A proper ideal I of R is called an (m, n)-absorbing ideal if whenever a
1⋯a
m
∈I for a
1,…, a
m
∈R∖U(R), then there are n of the a
i
’s whose product is in I. We investigate the stability of (m, n)-absorbing ideals with respect to various ring theoretic constructions and study (m, n)-absorbing ideals in several commutative rings. For example, in a Bézout ring or a Boolean ring, an ideal is an (m, n)-absorbing ideal if and only if it is an n-absorbing ideal, and in an almost Dedekind domain every (m, n)-absorbing ideal is a product of at most m − 1 maximal ideals.AbstractLet R be a commutative ring with 1 ≠ 0 and U(R) be the set of all unit elements of R. Let m, n be positive integers such that m > n. In this article, we study a generalization of n-absorbing ideals. A proper ideal I of R is called an (m, n)-absorbing ideal if whenever a
1⋯a
m
∈I for a
1,…, a
m
∈R∖U(R), then there are n of the a
i
’s whose product is in I. We investigate the stability of (m, n)-absorbing ideals with respect to various ring theoretic constructions and study (m, n)-absorbing ideals in several commutative rings. For example, in a Bézout ring or a Boolean ring, an ideal is an (m, n)-absorbing ideal if and only if it is an n-absorbing ideal, and in an almost Dedekind domain every (m, n)-absorbing ideal is a product of at most m − 1 maximal ideals.RURRmnmnnIRmna1a
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