On Two Classes of Modules Related to CS Trivial Extensions

2021/12/18 by Kourki, Farid, Tribak, Rachid
#16D10 #16D70 #16D80 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2112.09915

Abstract

All rings considered are commutative. In this article we introduce and study two notions of modules which are stronger than CS modules, namely weakly IN modules and strongly CS modules. Our main aim is to characterize when a trivial extension A=R∝ M (of a ring R by an R-module M) is a CS ring.

Related

• The strongly flat dimension of modules and rings
• On n-Trivial Extensions of Rings
• Modules in which pure submodule is essential in a direct summand
• CS-Rickart modules
• The category of modules on an n-trivial extension: the basic properties