吸收1的主子模块

Pub Date : 2021-02-24 DOI:10.2478/auom-2021-0045

E. Y. Çeli̇kel

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引用次数: 2

摘要

设R是一个非零单位元的交换环，M是一个酉R模。本文的目的是将吸收1元的主理想的概念推广到吸收1元的主子模。如果当非单位元素A, b∈R, M∈M且abm∈N时，则ab∈(N:RM)或M∈M - rad(N)，则M的固有子模N是一个吸收1的主子模。考虑了这类子模块的各种属性和特征。此外，还证明了吸1初级回避定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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1-absorbing primary submodules

Abstract Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule N of M is said to be a 1-absorbing primary submodule if whenever non-unit elements a, b ∈ R and m ∈ M with abm ∈ N, then either ab ∈ (N :RM) or m ∈ M − rad(N). Various properties and chacterizations of this class of submodules are considered. Moreover, 1-absorbing primary avoidance theorem is proved.

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