{"title":"Applications of $\\bigcap$-large pseudo N-injective acts in quasi-Frobenius monoid theory and its relationship with some classes of injectivity","authors":"S. Abdul-Kareem, A. A. Abdulkareem","doi":"10.56415/qrs.v30.16","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to review thoroughly the applications of ∩ -large pseudo N-injective acts in quasi-Frobenius monoid theory, and therefore, the relationship of ∩ -large pseudo N-injective acts with some class of injectivity is studied. Applications of the properties of ∩ -large pseudo injective acts in quasi-Frobenius monoid theory are proven. Also, it’s proved that the subsequent parity, every union (direct sum) of the two ∩ -large pseudo injective acts is a ∩ -large pseudo injective act if and only if every ∩ -large pseudo injective act is injective under Noetherian condition for a right monoid S. Additionally, we proved that the category of strongly ∩ -large pseudo N-injective right S-acts are going to be egalitarian to the category of projective right S-acts under monoid conditions. The connections between quasi injective and ∩ -large pseudo injective acts are investigated.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v30.16","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to review thoroughly the applications of ∩ -large pseudo N-injective acts in quasi-Frobenius monoid theory, and therefore, the relationship of ∩ -large pseudo N-injective acts with some class of injectivity is studied. Applications of the properties of ∩ -large pseudo injective acts in quasi-Frobenius monoid theory are proven. Also, it’s proved that the subsequent parity, every union (direct sum) of the two ∩ -large pseudo injective acts is a ∩ -large pseudo injective act if and only if every ∩ -large pseudo injective act is injective under Noetherian condition for a right monoid S. Additionally, we proved that the category of strongly ∩ -large pseudo N-injective right S-acts are going to be egalitarian to the category of projective right S-acts under monoid conditions. The connections between quasi injective and ∩ -large pseudo injective acts are investigated.