On weakly local rings

This article concerns a property of local rings and domains. A ring $R$ is called {\it weakly local} if for every $a\in R$, $a$ is regular or $1-a$ is regular, where a regular element means a non-zero-divisor. We study the structure of weakly local rings in relation to several kinds of factor rings...

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Bibliographic Details
Published in:한국수학논문집, 28(1) 2020, 28(1), , pp.65-73
Main Authors: Zhelin Piao, 류성주, 성효진, 윤상조
Format: Article
Language:English
Subjects:
수학
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Summary:This article concerns a property of local rings and domains. A ring $R$ is called {\it weakly local} if for every $a\in R$, $a$ is regular or $1-a$ is regular, where a regular element means a non-zero-divisor. We study the structure of weakly local rings in relation to several kinds of factor rings and ring extensions that play roles in ring theory. We prove that the characteristic of a weakly local ring is either zero or a power of a prime number. It is also shown that the weakly local property can go up to polynomial (power series) rings and a kind of Abelian matrix rings. KCI Citation Count: 0
ISSN:1976-8605
2288-1433
DOI:10.11568/kjm.2020.28.1.65