An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

This paper introduce and investigate the notion of FI− M− principally injective and FI− semi-
injective (fully invariant-semi injective) modules. Clearly FI− semi-injective module does not …

We study direct-sum decompositions of RD-projective modules. In particular, we investigate
the rings over which every RD-projective right module is a direct sum of cyclically presented …

In this study, all rings are commutative with non-zero identity and all modules are considered
to be unital. Let $ M $ be a left $ R $-module. A proper submodule $ N $ of $ M $ is called an …

Let S be a multiplicative subset of a ring R with unity. A unitary right R-module M is referred
to as S-injective if there exist an element s∈ S and an injective R-submodule Q of M such …

ABSTRACT A right R-module M is called simple-direct-injective if, whenever, A and B are
simple submodules of M with A≅ B, and B⊆⊕ M, then A⊆⊕ M. Dually, M is called simple …

Let R be a commutative ring. We investigate R-modules which can be written as finite sums
of second R-submodules (we call them second representable). The class of second …

A right module M is called direct-injective (or C2) if every submodule isomorphic to a
summand of M is itself a summand. Dually, a module M is called direct-projective (or D2) if …

Modules in which every submodule is isomorphic to a direct summand is called virtually
semisimple. In this article, we carry out a study of virtually semisimple modules over a …

In this paper, all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …