Finitely-cosmall Quotients

Authors : Berke KALEBOĞAZ

Pages : 226-234

Doi:10.16984/saufenbilder.1158987

View : 20 | Download : 8

Publication Date : 2023-02-28

Article Type : Research Paper

Abstract :In this paper, we first define the notion of finitely-cosmall quotient insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(singly-copartial isomorphism); from Z to Y with codomain U is a finitely insert ignore into journalissuearticles values(singly); split epimorphism. We also investigate the relation between pure-cosmall quotient and finitely-cosmall quotient insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(singly-cosmall quotient); morphism. Moreover, we obtain an example of right minimal morphisms by using finitely-cosmall quotient insert ignore into journalissuearticles values(singly-cosmall quotient); morphisms.
Keywords : Pure cosmall quotient morphisms, finitely cosmall quotient morphisms, right minimal morphisms