1. Throughout this note, all rings will have unit elements and all modules will be unitary. By a
Noetherian ring, we shall mean a right Noetherian ring. A non-zero right ideal in a ring will …

@ &f: izl,.,,(f--(m)) EIC~~* from 111 into its H-bidual is an isomorphism (resp.
monomorphism). For example, every finitely generated projective module is reflexive. An …

A module $ M $ is called a CS module if every submodule of $ M $ is essential in a direct
summand of $ M $. A ring $ R $ is said to be right (countably) $\Sigma $-CS if any direct sum …

Throughout this paper we suppose that all rings and modules are unitary. By J we denote
always the Jacobson radical of a ring S. The left (right, resp.) annihilator of X is denoted by Z …

And he has found two new classes of rings which are characterized by ideal theoretic
conditions: one is perfect rings with (*) and the other one is semiperfect rings with (*)*. In [9] …

Theorem (K6the-Cohen-Kaplansky). A commutative ring R has the property that each of its R-
modules is a direct sum of cyclic modules if and only if R is an artinian principal ideal ring …

Following, a ring R is called right almost-perfect if every flat right R-module is projective
relative to R. In this article, we continue the study of these rings and will find some new …

Let R be a ring and M a right R-module. M is called⊕-cofinitely supplemented if every
submodule N of M with M/N finitely generated has a supplement that is a direct summand of …

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 …