F补充模块

IF 0.3 Q4 MATHEMATICS, APPLIED

Algebra & Discrete Mathematics Pub Date : 2020-12-30 DOI:10.12958/adm1185

S. Özdemir

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引用次数: 1

摘要

设R是环，设M是左R模，设U，V，F是M的子模。我们称V为U在M中的F-补，如果V在集合F⊆X \8838M中是极小的，使得U+X=M，或者等价地，F≾V，U+V=M和UåV在V中是F-小的。如果M的每个子模都有F-补，那么我们称M为F-补模。在本文中，我们引入并研究了F-补充子模和（充分）F-补充模。我们给出了这些模的一些性质，并用它们的某些子模刻画了有限生成（充分）F-补模。

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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F-supplemented modules

Let R be a ring, let M be a left R-module, and let U,V,F be submodules of M with F proper. We call V an F-supplement of U in M if V is minimal in the set F⊆X⊆M such that U+X=M, or equivalently, F⊆V, U+V=M and U∩V is F-small in V. If every submodule of M has an F-supplement, then we call M an F-supplemented module. In this paper, we introduce and investigate F-supplement submodules and (amply) F-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) F-supplemented modules in terms of their certain submodules.

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来源期刊

Algebra & Discrete Mathematics MATHEMATICS, APPLIED-

CiteScore

0.50

自引率

0.00%

发文量