![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
Let M be a module and K a submodule of a module N in σ[M]. We call K a δ–M-small submodule of N if whenever N = K + L, N/L is M-singular for any submodule L of N, we have N = L. Also we call N a δ–M-small module if N is a δ–M-small submodule of its M-injective hull. In this article, we consider , the reject of
ℳ in N, where
ℳ is the class of all δ–M-small modules. We investigate the properties of
and consider the torsion theory τδ V
in σ[M] cogenerated by
ℳ. We compare the τδ V
and the torsion theory τ
V
cogenerated by M-small modules and finally we give a characterization of GCO-modules.
Notes
Communicated by R. Wisbauer.