吸收1的主子模块

IF 0.8 4区数学 Q2 MATHEMATICS

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica 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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来源期刊

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is founded by Mirela Stefanescu and Silviu Sburlan in 1993 and is devoted to pure and applied mathematics. Published by Faculty of Mathematics and Computer Science, Ovidius University, Constanta, Romania.