Remarks on \(\alpha \)-strongly irreducible ideals
type: Item
instance of: scholarly article
title: Remarks on \(\alpha \)-strongly irreducible ideals
zbMATH Open document ID: 1229.13006
author: F. Fatahi
author: M. J. Nikmehr
published in: Frontiers of Mathematics in China
publication date: 2011-11-04T00:00:00Z
review text: In the paper under review, the authors find some results on the notion of \(\alpha \)-strongly irreduciblility introduced by \textit{X. Lu} and \textit{H. Qin} [Southeast Asian Bull. Math. 32, No. 2, 299--303 (2008; Zbl 1174.13005)]. It is proved that a submodule \(N\) of a multiplication module \(M\) is an \(\alpha \)-strongly irreducible submodule iff its colon ideal is an \(\alpha \)-strongly irreducible ideal. Also, this concept is considered in the localization construction.
reviewed by: Naser Zamani
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 5968165
zbMATH Keywords: \(\alpha \)-irreducible
zbMATH Keywords: \(\alpha \)-strongly irreducible
zbMATH Keywords: ideal
zbMATH Keywords: faithful module
zbMATH Keywords: multiplication module
MaRDI profile type: Publication
full work available at URL: s11464-011-0156-3
OpenAlex ID: W2167406516
cites work: STRONGLY IRREDUCIBLE IDEALS
cites work: Multiplication modules
cites work: Strongly irreducible ideals of a commutative ring
cites work: Q4224184
cites work: Some remarks on multiplication modules
cites work: Q4049223
cites work: Q5732721
DOI: 10.1007/S11464-011-0156-3
description: scientific article; zbMATH DE number 5968165