关于所有子模块都有唯一闭包的模块的一些注意事项

IF 0.9 4区数学 Q1 Mathematics

Miskolc Mathematical Notes Pub Date : 2022-01-01 DOI:10.18514/mmn.2022.3876

Özgür Taşdemir

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引用次数: 0

摘要

如果模块M的每个子模块都有一个唯一的闭包，则模块M称为uc模块。在本文中，我们用UC-模建立了一些已经被广泛研究的环类的新的刻画，并证明了UC不是Morita不变性质。此外，我们还研究了环的优秀扩展下uc模的行为。

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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Some notes on modules in which all submodules have a unique closure

A module M is called a UC-module if whenever every submodule of M has a unique closure. In this paper, we establish new characterizations of several well-studied classes of rings in terms of UC-modules, and show that UC is not a Morita invariant property. In addition, we study the behaviour of UC-modules under excellent extensions of rings.

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来源期刊

Miskolc Mathematical Notes Mathematics-Algebra and Number Theory

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： Miskolc Mathematical Notes, HU ISSN 1787-2405 (printed version), HU ISSN 1787-2413 (electronic version), is a peer-reviewed international mathematical journal aiming at the dissemination of results in many fields of pure and applied mathematics.