{"title":"关于$\\mathcal{F}$-同胚态射","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":"{\"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}","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}
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 $\mathcal{F}$.