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 …

Let R be a ring and M be an R-module. In this paper we investigate modules M such that
every (simple) cosingular R-module is M-projective. We prove that every simple cosingular …

Let M be a right R-module,\cal M the class of all M-small modules, and P a projective cover
of M in σ M. We consider the torsion theories\cal M=(\cal T _\cal M,\cal F _\cal M),\tau_V=(\cal …

As a generalization of essential submodules Zhou defines a µ-essential submodule
provided it has a non-zero intersection with any non-zero submodule in µ for any class µ. Let …

As a generalization of essential submodules Zhou defines a mu-essential submodule
provided it has a non-zero intersection with any non-zero submodule in it for any class p. Let …

Let M be a right R-module and N∈ σ [M]. A submodule K of N is called δ-M-small if,
whenever N= K+ X with N/XM-singular, we have N= X. N is called a δ-M-small module if N≅ …

Abstract top Let M be a module and μ be a class of modules in Mod-R which is closed under
isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] …