{"title":"A new member of Nicholson's morphic folks","authors":"Truong Cong Quynh , M. Tamer Koşan , Jan Žemlička","doi":"10.1016/j.jalgebra.2024.10.009","DOIUrl":null,"url":null,"abstract":"<div><div>The main aim of the paper is to describe the structure of modules and corresponding rings satisfying the property (<em>P</em>), which says that <span><math><mi>M</mi><mo>/</mo><mi>im</mi><mo>(</mo><mi>α</mi><mo>)</mo></math></span> is embeddable into <span><math><mi>ker</mi><mo></mo><mo>(</mo><mi>α</mi><mo>)</mo></math></span> for each endomorphism <em>α</em> and which generalizes the morphic property. In particular, it is proved that the class of rings with the property (<em>P</em>) is closed under taking products and summands and contains unit regular rings. We also explain connections between the virtually internal cancellation property and the property (<em>P</em>) and characterize the structure of particular classes of rings satisfying the property (<em>P</em>).</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"664 ","pages":"Pages 268-287"},"PeriodicalIF":0.8000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324005477","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The main aim of the paper is to describe the structure of modules and corresponding rings satisfying the property (P), which says that is embeddable into for each endomorphism α and which generalizes the morphic property. In particular, it is proved that the class of rings with the property (P) is closed under taking products and summands and contains unit regular rings. We also explain connections between the virtually internal cancellation property and the property (P) and characterize the structure of particular classes of rings satisfying the property (P).
期刊介绍:
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.