P-正则环和P-局部环

Q4 Mathematics

Journal of Algebra and Related Topics Pub Date : 2021-06-01 DOI:10.22124/JART.2021.17609.1230

H. Hakmi

{"title":"P-正则环和P-局部环","authors":"H. Hakmi","doi":"10.22124/JART.2021.17609.1230","DOIUrl":null,"url":null,"abstract":"This paper is a continuation of study rings relative to rightideal, where we study the concepts of regular and local ringsrelative to right ideal. We give some relations between $P-$local($P-$regular) and local (regular) rings. New characterizationobtained include necessary and sufficient conditions of a ring $R$to be regular, local ring in terms $P-$regular, $P-$local ofmatrices ring $M_{2}(R)$. Also, We proved that every ring is localrelative to any maximal right ideal of it.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"9 1","pages":"1-19"},"PeriodicalIF":0.0000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"P-Regular and P-Local Rings\",\"authors\":\"H. Hakmi\",\"doi\":\"10.22124/JART.2021.17609.1230\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is a continuation of study rings relative to rightideal, where we study the concepts of regular and local ringsrelative to right ideal. We give some relations between $P-$local($P-$regular) and local (regular) rings. New characterizationobtained include necessary and sufficient conditions of a ring $R$to be regular, local ring in terms $P-$regular, $P-$local ofmatrices ring $M_{2}(R)$. Also, We proved that every ring is localrelative to any maximal right ideal of it.\",\"PeriodicalId\":52302,\"journal\":{\"name\":\"Journal of Algebra and Related Topics\",\"volume\":\"9 1\",\"pages\":\"1-19\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra and Related Topics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22124/JART.2021.17609.1230\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Related Topics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22124/JART.2021.17609.1230","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

本文是关于右理想的研究环的延续，在这里我们研究了正则环和局部环的概念。我们给出了$P-$局部（$P-$正则）环和局部（正则）环之间的一些关系。得到的新刻画包括环$R$为正则的充要条件，关于矩阵环$M_{2}（R）$的$P-$正则、$P-$局部的局部环。此外，我们还证明了每个环相对于它的任何极大右理想都是局部相对的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

P-Regular and P-Local Rings

This paper is a continuation of study rings relative to rightideal, where we study the concepts of regular and local ringsrelative to right ideal. We give some relations between $P-$local($P-$regular) and local (regular) rings. New characterizationobtained include necessary and sufficient conditions of a ring $R$to be regular, local ring in terms $P-$regular, $P-$local ofmatrices ring $M_{2}(R)$. Also, We proved that every ring is localrelative to any maximal right ideal of it.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Algebra and Related Topics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

16 weeks