In this article, we study the C 4-and D 4-modules in terms of perspective direct summands,
providing new characterizations and results. Endomorphism rings of C 4-modules and …

Recently, in a series of papers “simple” versions of direct-injective and direct-projective
modules have been investigated. These modules are termed as “simple-direct-injective” and …

A new category equivalence is proved in this paper, involving the two distinct categories of
modules, the covariant and the contravariant, respectively, released by Higgins and …

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 …

In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give
equivalent conditions for SIP and SSP modules; establish connections between the class of …

Let A be a class of some right R‐modules that is closed under isomorphisms, and let M be a
right R‐module. Then M is called A‐D3 if, whenever N and K are direct summands of M with …

The notion of simple-direct-injective modules which are a generalization of injective
modules unifies $ C2 $ and $ C3 $-modules. In the present paper, we introduce the notion of …

A module M is called a simple-direct-injective module if, whenever A and B are simple
submodules of M with A≅ B and B is a direct summand of M, then A is a direct summand of …

DIRECT PROJECTIVE MODULES, DIRECT INJECTIVE MODULES, AND THEIR
GENERALIZATIONS AN Abyzov, AA Tuganbaev, DT Tapkin, and Page 1 Journal of …

In the present paper, we study simple-direct-injective modules and simple-direct-projective
modules over a formal matrix ring K=\left (R&M\N&S), where M is an (R, S)-bimodule and N …