In this paper, we study some more properties on direct-injective modules in the context of
endoregular, SSP and SIP modules. We find the equivalent condition for a directinjective …

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 …

In this paper we study M-small principally injective (in short, M-sp-injective) module which is
the generalization of M-principally injective module. We prove that if M is finite dimensional …

A left module $ M $ over an arbitrary ring is called an $\mathcal {RD} $-module (or an
$\mathcal {RS} $-module) if every submodule $ N $ of $ M $ with ${\rm Rad}(M)\subseteq N …

In this paper, the authors give a partial characterization of invertible, dense and projective
submodules. In the final section, they give the equivalent conditions to be invertible, dense …

An R-module is a simple divisible module if it is a nonzero divisible module that has no
proper non-zero divisible submodules. We study simple divisible modules and their …

We define prime uniserial modules as a generalization of uniserial modules. We say that an
R-module M is prime uniserial (℘-uniserial) if its prime submodules are linearly ordered by …

Throughout this paper R will denote a ring with idenity element and M a unitary right module
over R. An R-module M is said to be direct injective if and only if given direct summand N of …

A left R-module M is said to be left singly injective if Ext R 1 (F/K, M)= 0 for any cyclic
submodule K of any finitely generated free left R-module F. In this paper, we study the notion …

In this paper, we generalize the concept of direct-injective modules to fi nite-direct-injective
modules. Various basic properties of these modules are studied. We show that the class of fi …