Strongly sum 2-irreducible submodules of a module
type: Item
instance of: scholarly article
title: Strongly sum 2-irreducible submodules of a module
zbMATH Open document ID: 1506.13016
published in: São Paulo Journal of Mathematical Sciences
publication date: 2022-12-02T00:00:00Z
review text: A non-zero submodule \(N\) of a module \(M\) over a commutative ring \(R\) is called sum 2-irreducible if whenever it is the sum of three submodules of \(M\), it is already the sum of two of the three. This notion was introduced in [\textit{F. Farshadifar} and \textit{H. Ansari-Toroghy}, Jordan J. Math. Stat. 14, No. 3, 545--554 (2021; Zbl 1488.13035)]. In the present paper, the authors define and study the concept of strongly sum 2-irreducibility. A non-zero submodule \(N\) of \(M\) is strongly sum 2-irreducible if whenever it is contained in the sum of three submodules of \(M\), it is already contained in the sum of two of the three. The main result, Theorem 1, characterizes strongly sum 2-irreducible submodules in terms of completely irreducible submodules: submodules of \(M\) that cannot be written as the intersection of a family of strictly larger submodules of \(M\). Characterizations of strongly sum 2-irreducibility are provided for submodules \(N\) having certain additional properties, and for submodules of \(M\) in the case that \(R\) is a finite product of constituent rings.
reviewed by: Matthé van der Lee
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 13C99
zbMATH DE Number: 7626125
zbMATH Keywords: sum 2-irreducible submodule
zbMATH Keywords: strongly sum 2-irreducible submodule
zbMATH Keywords: irreducible ideal
zbMATH Keywords: strongly 2-irreducible ideal
author: F. Farshadifar
author: H. Ansari-Toroghy
MaRDI profile type: Publication
full work available at URL: s40863-021-00211-w
OpenAlex ID: W3123012454
Wikidata QID: Q121619719
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DOI: 10.1007/S40863-021-00211-W
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description: scientific article; zbMATH DE number 7626125