CHARACTERIZATIONS OF SOME CLASSES OF RINGS VIA LOCALLY SUPPLEMENTED MODULES

Authors : Farid KOURKİ, Rachid TRİBAK

Pages : 178-193

Doi:10.24330/ieja.663060

View : 19 | Download : 11

Publication Date : 2020-01-07

Article Type : Research Paper

Abstract :We introduce the notion of locally supplemented modules insert ignore into journalissuearticles values(i.e., modules for which every finitely generated submodule is supplemented);. We show that a module $M$ is locally supplemented if and only if $M$ is a sum of local submodules. We characterize several classes of rings in terms of locally supplemented modules. Among others, we prove that a ring $R$ is a Camillo ring if and only if every finitely embedded $R$-module is locally supplemented. It is also shown that a ring $R$ is a Gelfand ring if and only if every $R$-module having a finite Goldie dimension is locally supplemented.
Keywords : Camillo ring, Gelfand ring, locally supplemented module, semiperfect ring, supplemented module