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.
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JALAL ABADI, B.Z., MOGHIMI, H.F. On (m, n)-absorbing ideals of commutative rings. Proc Math Sci 127, 251–261 (2017). https://doi.org/10.1007/s12044-016-0323-2
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DOI: https://doi.org/10.1007/s12044-016-0323-2