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arXiv · 2007.01103

On 1-absorbing prime submodules

Emel Aslankarayigit Ugurlu
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Abstract

In this study, we aim to introduce the concept of a 1-absorbing prime submodule of an unital module over a commutative ring with a non-zero identity. Let M be an R-module and N be a proper submodule of M. For all non-unit elements a, b in R and m in M if abm in N, either ab in (N : M) or m in N, then N is called 1-absorbing prime submodule of M. We show that the new concept is a generalization of prime submodules at the same time it is a kind of special 2-absorbing submodule. In addition to some properties of a 1-absorbing prime submodule, we obtain a characterization of it in a multiplication module.

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Emel Aslankarayigit Ugurlu. 2020-07-02. On 1-absorbing prime submodules. https://arxiv.org/abs/2007.01103

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