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On ϕ-β-Absorbing Submodules
Author(s)
Date Issued
January 1, 2022
Type
Article
Abstract
In this paper, we extend the concept of β-absorbing submodules to ϕ-β-absorbing submodules over a commutative ring with nonzero identity which is a generalization of 2-absorbing submodules. Let S(M) be the set of all submodules of M and ϕ : S(M) → S(M)∪{∅} be a function. A proper submodule P of M is called a ϕ-β-absorbing submodule, if for each r, s ∈ R and m ∈ M with rsm ∈ P\ϕ(P), then rs + rs ∈ (P : M) or r(m + m) ∈ P or s(m + m) ∈ P. Some of the properties and characterizations of ϕ-β-absorbing submodules are investigated.
Citation
European Journal of Pure and Applied Mathematics, 15(1), 328-334, 2022