{"title":"\"ON CLEAN FREE MODULES AND A CHARACTERIZATION OF CLEAN RINGS\"","authors":"Esmaeil Rostami, S. Hedayat","doi":"10.59277/mrar.2023.25.75.1.103","DOIUrl":null,"url":null,"abstract":"\"In this paper, the concept of clean ring is generalized to modules. We call a free R-module, Rn, clean, whenever every element of Rn can be written as the sum of a unimodular and an idempotent row. We show that when R is Noetherian, the R-module Rn is clean if and only if R can be expressed as a finite direct product of indecomposable rings Ri, say R = Lt i=1 Ri, such that each Ri has at most 2n − 1 maximal ideals. We also give a new characterization of clean rings.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"44 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Reports","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.59277/mrar.2023.25.75.1.103","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
"In this paper, the concept of clean ring is generalized to modules. We call a free R-module, Rn, clean, whenever every element of Rn can be written as the sum of a unimodular and an idempotent row. We show that when R is Noetherian, the R-module Rn is clean if and only if R can be expressed as a finite direct product of indecomposable rings Ri, say R = Lt i=1 Ri, such that each Ri has at most 2n − 1 maximal ideals. We also give a new characterization of clean rings."
期刊介绍：
The journal MATHEMATICAL REPORTS (formerly STUDII SI CERCETARI MATEMATICE) was founded in 1948 by the Mathematics Section of the Romanian Academy. It appeared under its first name until 1998 and received the name of Mathematical Reports in 1999. It is now published in one volume a year, consisting in 4 issues. The current average total number of pages is 500.
Our journal MATHEMATICAL REPORTS publishes original mathematical papers, written in English. Excellent survey articles may be also accepted. The editors will put strong emphasis on originality, quality and applicability.
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