Finitely-cosmall Quotients
In this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient) morphisms. Then we give a characterization of this new concept. We show that an epimorphism p:Y→U is a finitely-cosmall quotient (singly-cosmall quotient) if and only if for any right R-module Z any morp...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sakarya University
2023-02-01
|
| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2584172 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850252357227511808 |
|---|---|
| author | Berke Kaleboğaz |
| author_facet | Berke Kaleboğaz |
| author_sort | Berke Kaleboğaz |
| collection | DOAJ |
| description | In this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient) morphisms. Then we give a characterization of this new concept. We show that an epimorphism p:Y→U is a finitely-cosmall quotient (singly-cosmall quotient) if and only if for any right R-module Z any morphism g:Z→Y such that pg is a finitely-copartial isomorphism (singly-copartial isomorphism) from Z to Y with codomain U is a finitely (singly) split epimorphism. We also investigate the relation between pure-cosmall quotient and finitely-cosmall quotient (singly-cosmall quotient) morphisms. We prove that over a right Noetherian ring R, an epimorphism p:Y→U is a pure-cosmall quotient morphism if and only if p is a finitely-cosmall quotient (singly-cosmall quotient) morphism. Moreover, we obtain an example of right minimal morphisms by using finitely-cosmall quotient (singly-cosmall quotient) morphisms. |
| format | Article |
| id | doaj-art-001f9f705e8d4ed39cccf62e9aaecab8 |
| institution | OA Journals |
| issn | 2147-835X |
| language | English |
| publishDate | 2023-02-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-001f9f705e8d4ed39cccf62e9aaecab82025-08-20T01:57:40ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2023-02-0127122623410.16984/saufenbilder.115898728Finitely-cosmall QuotientsBerke Kaleboğaz0https://orcid.org/0000-0002-4903-2244Hacettepe ÜniversitesiIn this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient) morphisms. Then we give a characterization of this new concept. We show that an epimorphism p:Y→U is a finitely-cosmall quotient (singly-cosmall quotient) if and only if for any right R-module Z any morphism g:Z→Y such that pg is a finitely-copartial isomorphism (singly-copartial isomorphism) from Z to Y with codomain U is a finitely (singly) split epimorphism. We also investigate the relation between pure-cosmall quotient and finitely-cosmall quotient (singly-cosmall quotient) morphisms. We prove that over a right Noetherian ring R, an epimorphism p:Y→U is a pure-cosmall quotient morphism if and only if p is a finitely-cosmall quotient (singly-cosmall quotient) morphism. Moreover, we obtain an example of right minimal morphisms by using finitely-cosmall quotient (singly-cosmall quotient) morphisms.https://dergipark.org.tr/tr/download/article-file/2584172pure-cosmall quotient morphismsfinitely-cosmall quotient morphismsright minimal morphismspure-cosmall quotient morphismsfinitely-cosmall quotient morphismsright minimal morphisms |
| spellingShingle | Berke Kaleboğaz Finitely-cosmall Quotients Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi pure-cosmall quotient morphisms finitely-cosmall quotient morphisms right minimal morphisms pure-cosmall quotient morphisms finitely-cosmall quotient morphisms right minimal morphisms |
| title | Finitely-cosmall Quotients |
| title_full | Finitely-cosmall Quotients |
| title_fullStr | Finitely-cosmall Quotients |
| title_full_unstemmed | Finitely-cosmall Quotients |
| title_short | Finitely-cosmall Quotients |
| title_sort | finitely cosmall quotients |
| topic | pure-cosmall quotient morphisms finitely-cosmall quotient morphisms right minimal morphisms pure-cosmall quotient morphisms finitely-cosmall quotient morphisms right minimal morphisms |
| url | https://dergipark.org.tr/tr/download/article-file/2584172 |
| work_keys_str_mv | AT berkekalebogaz finitelycosmallquotients |