强烈清洁的半成品

IF 0.8 4区综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2024-04-28 DOI:10.1007/s40010-024-00875-x

D. Das, S. Kar

{"title":"强烈清洁的半成品","authors":"D. Das, S. Kar","doi":"10.1007/s40010-024-00875-x","DOIUrl":null,"url":null,"abstract":"<div>In this paper, we study the concept of strongly clean semiring. Let S be a semiring. An element \\(a\\in S\\) is called strongly clean if \\(a = e + u\\) with e an idempotent in S and u a unit in S such that \\(eu=ue\\). A semiring S is said to be strongly clean if every nonzero element of S is strongly clean. We mainly study the notion of strongly clean semiring and obtain some important characterizations of strongly clean semiring in connection with exchange semiring, antisimple semiring and inverse semiring.</div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"94 2","pages":"249 - 258"},"PeriodicalIF":0.8000,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Strongly Clean Semiring\",\"authors\":\"D. Das, S. Kar\",\"doi\":\"10.1007/s40010-024-00875-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>In this paper, we study the concept of strongly clean semiring. Let S be a semiring. An element \\\\(a\\\\in S\\\\) is called strongly clean if \\\\(a = e + u\\\\) with e an idempotent in S and u a unit in S such that \\\\(eu=ue\\\\). A semiring S is said to be strongly clean if every nonzero element of S is strongly clean. We mainly study the notion of strongly clean semiring and obtain some important characterizations of strongly clean semiring in connection with exchange semiring, antisimple semiring and inverse semiring.</div>\",\"PeriodicalId\":744,\"journal\":{\"name\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"volume\":\"94 2\",\"pages\":\"249 - 258\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40010-024-00875-x\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-024-00875-x","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们将研究强干净配线的概念。设 S 是一个配系。如果 \(a = e + u\) 中的 e 是 S 中的一个幂等元素，而 u 是 S 中的一个单位，使得 \(eu=ue\) 称为强干净元素。如果 S 中的每个非零元素都是强干净的，那么我们就说 S 是强干净的。我们主要研究强干净配线的概念，并得到强干净配线与交换配线、反简单配线和逆配线相关的一些重要特征。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Strongly Clean Semiring

In this paper, we study the concept of strongly clean semiring. Let S be a semiring. An element \(a\in S\) is called strongly clean if \(a = e + u\) with e an idempotent in S and u a unit in S such that \(eu=ue\). A semiring S is said to be strongly clean if every nonzero element of S is strongly clean. We mainly study the notion of strongly clean semiring and obtain some important characterizations of strongly clean semiring in connection with exchange semiring, antisimple semiring and inverse semiring.