A variation of stable range one
type: Item
instance of: scholarly article
title: A variation of stable range one
DOI: 10.1080/00927872.2024.2332387
author: Yiqiang Zhou
published in: Communications in Algebra
publication date: 2024-08-29T00:00:00Z
review text: The reviewed article is devoted to the examination of a variation of stable range one for an associative unital ring \(R\), concerning its set of all nilpotent elements \(\mathrm{nil}(R)\).\N\NIn fact, an element \(a\) in a ring \(R\) is said to have \textit{left nilpotent stable range 1} if, whenever \(Ra+Rb=R\) for any \(b \in R\), there exists \(r \in \mathrm{nil}(R)\) such that \(a+rb\in U(R)\).\N\NSome interesting results are obtained (see, respectively, Propositions 2.5, 2.6 and 2.7; Propositions 3.2, 3.3 and 3.4; Theorem 4.2, Corollaries 4.5, 4.6) as well as certain valuable examples are provided (see, respectively, Examples 2.4; 3.1; 4.3, 4.4).
reviewed by: Peter Danchev
Mathematics Subject Classification ID: 16U99
zbMATH DE Number: 7903239
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7903239