On classical 1-absorbing prime submodules
arxiv(2024)
Abstract
In this study, we aim to introduce the concept of classical 1-absorbing prime
submodules of a nonzero unital module M over a commutative ring A with
unity. A proper submodule P of M is said to be a classical 1-absorbing
prime submodule, if for each m∈ M and nonunits a,b,c∈ A, abcm∈ P
implies that abm∈ P or cm∈ P. We give many examples and properties of
classical 1-absorbing prime submodules. Also, we investiage the classical
1-absorbing prime submodules of tensor product F⊗ M of a (faithfully)
flat A-module F and any A-module M. Furthermore, we determine classical
prime, classical 1-absorbing prime and classical 2-absorbing submodules of
amalgamated duplication M⋈ I of an A-module M along an ideal I.
Also, we characterize local rings (A,𝔪) with 𝔪^2=0
in terms of classical 1-absorbing prime submodules.
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