Let t be a radical for the category of left R-modules for a ring R. If M is a t-coatomic module,
that is, if M has no nonzero t-torsion factor module, then t (M) is small in M. If V is a t …

A module M is called (cofinitely) Rad-⊕-supplemented if every (cofinite) submodule of M
has a Rad-supplement that is a direct summand of M. We prove that if M is a coatomic …

A module $ M $ is called $ emph {H} $-cofinitely supplemented if for every cofinite
submodule $ E $(ie $ M/E $ is finitely generated) of $ M $ there exists a direct summand $ D …

In the present paper, we define generalized (amply) cofinitely supplemented modules, and
generalized⊕-cofinitely supplemented modules are defined as a generalization of (amply) …

In this paper we provide various properties of Rad-⊕-supplemented modules. In particular,
we prove that a projective module M is Rad-⊕-supplemented if and only if M is⊕ …

Let R be a ring and M be a left R− module. In this work some properties of (amply) cofinitely
Rad-supplemented modules are developed. It is shown that if M contains a nonzero semi …

We study the properties of⊕-cofinitely radical supplemented modules, or, briefly, cgs⊕-
modules. It is shown that a module with summand sum property (SSP) is cgs⊕ if and only if …

Over a general ring, an R-module is w-supplemented if and only if amply w-supplemented. It
is proved that over a local Dedekind domain, all modules are w-supplemented and over a …

In this paper we introduce w-coatomic modules and some of their properties. We prove that
the finite sum of w-coatomic modules is w-coatomic. It is shown that w-coatomic modules are …

Throughout the whole text, R will always denote an associative ring with identity. By a
module M, we shall mean a left unitary R-module. Let M be such a module, we shall write …