2016/09/13 by Abyzov Adel Nailevich, Nailevich, Abyzov Adel, Truong Cong Quynh +3
Mathematics · #16D40 #16D80 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16D40 #msc:16D80
paper · pdf · doi:10.48550/arxiv.1609.04052
arxiv created 2016/09/13 · arxiv updated 2016/09/15
The aim of this paper is to study the notions of A-C3 and A-D3 modules for some class A of right modules. Several characterizations of these modules are provided and used to describe some well-known classes of rings and modules. For example, a regular right R-module F is a V-module if and only if every F-cyclic module M is an A-C3 module where A is the class of all simple submodules of M. Moreover, let R be a right artinian ring and A, a class of right R-modules with local endomorphisms, containing all simple right R-modules and closed under isomorphisms. If all right R-modules are A-injective, then R is a serial artinian ring with J2(R)=0 if and only if every A-C3 right R-module is quasi-injective, if and only if every A-C3 right R-module is C3.