\(\psi\)-second submodules of a module
type: Item
instance of: scholarly article
title: \(\psi\)-second submodules of a module
zbMATH Open document ID: 1461.13007
published in: Beiträge zur Algebra und Geometrie
publication date: 2020-08-03T00:00:00Z
review text: Let \(R\) be a commutative ring with identity and let \(M\) be an \(R\)-module. A non-zero submodule \(N\) of \(M\) is said to be second if for each \(a\in R\), the homomorphism \(\varphi: N\rightarrow N\) with \(\varphi(x)=ax\) for \(x\in N\) is either surjective or zero. In the paper under review the authors introduce and study \(\psi\)-second submodule as follows: Let \(\psi: S(M)\rightarrow S(M)\cup\{\varnothing\}\) be a function, where \(S(M)\) denote the set of all submodules of M. A non-zero submodule \(N\) of \(M\) is called \(\psi\)-second submodule of \(M\) if for any \(r\in R\) and \(K\) a submodule of \(M\), \(rN\subseteq K\), and \(r\psi(N)\nsubseteq K\) implies \(N\subseteq K\) or \(rN = 0\).
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 7227037
zbMATH Keywords: second submodule
zbMATH Keywords: \(\phi\)-prime ideal
zbMATH Keywords: weak second submodule
zbMATH Keywords: \(\psi\)-second submodule
author: F. Farshadifar
author: H. Ansari-Toroghy
reviewed by: Siamak Yassemi
MaRDI profile type: Publication
full work available at URL: s13366-020-00495-7
OpenAlex ID: W3010221387
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cites work: Q5208686
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cites work: φ-PRIME SUBMODULES
DOI: 10.1007/S13366-020-00495-7
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description: scientific article; zbMATH DE number 7227037