Nonnil-Laskerian rings
type: Item
instance of: scholarly article
title: Nonnil-Laskerian rings
zbMATH Open document ID: 1498.13052
author: Samir Moulahi
published in: Beiträge zur Algebra und Geometrie
publication date: 2022-10-28T00:00:00Z
review text: Let \(R\) be a commutative ring with unity and \(\mathrm{Nil}(R)\) its nilradical; i.e, the set of its nilpotent elements. An ideal \(I\) of \(R\) is said decomposable if it is an intersection of finite number of primary ideals. It is nonnil if \(I\not\subseteq\mathrm{Nil}(R)\). The ring \(R\) is said nonnil-Laskerian if each nonnil ideal is decomposable. In this paper, the author show that the concepts of Laskerian and nonnil-Laskerian rings are different but they share many interesting properties. However, they differ when we consider the polynomial and the power series extensions.
reviewed by: Ali Benhissi
Mathematics Subject Classification ID: 13E99
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13F25
zbMATH DE Number: 7608931
zbMATH Keywords: Laskerian rings
zbMATH Keywords: Nonnil-Noetherian rings
zbMATH Keywords: Nonnil-Laskerian rings
zbMATH Keywords: nilradical of ring
zbMATH Keywords: divided prime ideal
MaRDI profile type: Publication
full work available at URL: s13366-021-00603-1
OpenAlex ID: W3206376659
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DOI: 10.1007/S13366-021-00603-1
description: scientific article; zbMATH DE number 7608931