Pure-cosmall quotient morphisms finitely-cosmall quotient morphisms right minimal morphisms
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.
Pure-cosmall quotient morphisms finitely-cosmall quotient morphisms right minimal morphisms
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 28 Şubat 2023 |
Gönderilme Tarihi | 8 Ağustos 2022 |
Kabul Tarihi | 3 Ocak 2023 |
Yayımlandığı Sayı | Yıl 2023 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.