{"title":"Cancellation Property for Acts Over Monoids","authors":"Kamal Ahmadi, Ali Madanshekaf","doi":"10.1007/s40995-024-01728-3","DOIUrl":null,"url":null,"abstract":"<div><p>The cancellation property in the theory of actions over a monoid is introduced and examined in this paper. We will find some significant classes of acts which are cancellable. In addition, we give a characterization of cancellable acts. Then, we prove that every act is cancellable if and only if it is internally cancellable. Finally, using significant properties of refinement monoids, we show that any Dedekind-finite <i>S</i>-act is cancellable and it has also multiplicative cancellation in the category of Dedekind-finite <i>S</i>-acts with a unique zero.</p></div>","PeriodicalId":600,"journal":{"name":"Iranian Journal of Science and Technology, Transactions A: Science","volume":"49 2","pages":"409 - 417"},"PeriodicalIF":1.4000,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iranian Journal of Science and Technology, Transactions A: Science","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s40995-024-01728-3","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
The cancellation property in the theory of actions over a monoid is introduced and examined in this paper. We will find some significant classes of acts which are cancellable. In addition, we give a characterization of cancellable acts. Then, we prove that every act is cancellable if and only if it is internally cancellable. Finally, using significant properties of refinement monoids, we show that any Dedekind-finite S-act is cancellable and it has also multiplicative cancellation in the category of Dedekind-finite S-acts with a unique zero.
期刊介绍:
The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences