{"title":"On $\\mathcal{F}$-cosmall morphisms","authors":"Berke Kalebog̃az, D. Keskin Tütüncü","doi":"10.31801/cfsuasmas.1061084","DOIUrl":null,"url":null,"abstract":"In this paper, we first define the notion of $\\mathcal{F}$-cosmall quotient for an additive exact substructure $\\mathcal{F}$ of an exact structure $\\mathcal{E}$ in an additive category $\\mathcal{A}$. We show that every $\\mathcal{F}$-cosmall quotient is right minimal in some cases. We also give the definition of $\\mathcal{F}$-superfluous quotient and we relate it the approximation of modules. As an application, we investigate our results in a pure-exact substructure $\\mathcal{F}$.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.1061084","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we first define the notion of $\mathcal{F}$-cosmall quotient for an additive exact substructure $\mathcal{F}$ of an exact structure $\mathcal{E}$ in an additive category $\mathcal{A}$. We show that every $\mathcal{F}$-cosmall quotient is right minimal in some cases. We also give the definition of $\mathcal{F}$-superfluous quotient and we relate it the approximation of modules. As an application, we investigate our results in a pure-exact substructure $\mathcal{F}$.