论文的补充:具有有限多子模块的模块

IF 0.5 Q3 MATHEMATICS

International Electronic Journal of Algebra Pub Date : 2020-07-14 DOI:10.24330/ieja.768272

Gabriel Picavet, M. Picavet-L'Hermitte

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引用次数: 0

摘要

论文摘要:“G. Picavet和M. Picavet- l 'Hermitte，具有有限多子模的模，Int.”电子。代数学报，19(2016)，119-131。:我们刻画了环扩展$R \子集S$具有FCP (FIP)，其中$S$是某个$R$-模的理想化。作为副产品，我们展示了具有有限多个子模块的模块的特征。我们的工具是最小环态射，而环上的阿提尼条件是普遍存在的。$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

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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AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES

Abstract of the paper: "G. Picavet and M. Picavet-L'Hermitte, Modules with finitely many submodules, Int. Electron. J. Algebra, 19 (2016), 119-131.": We characterize ring extensions $R \subset S$ having FCP (FIP), where $S$ is the idealization of some $R$-module. As a by-product we exhibit characterizations of the modules that have finitely many submodules. Our tools are minimal ring morphisms, while Artinian conditions on rings are ubiquitous. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

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来源期刊

International Electronic Journal of Algebra MATHEMATICS-

CiteScore

0.90

自引率

16.70%

发文量

审稿时长

36 weeks

期刊介绍： The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.