ABSTRACT. Let R be a ring with identity and M a right R-module. Let E (M) denote the
injective hull of M and Z'(M):= MORadE (M). We say M has*-radical if Z (M)= RadM. In this …

A right $ R $-module $ M $ is called $ R $-projective provided that it is projective relative to
the right $ R $-module $ R_ {R} $. This paper deals with the rings whose all nonsingular …

Let $ R $ be a ring and $ M $ be an $ R $-module. In this paper we investigate modules $ M
$ such that every (simple) cosingular $ R $-module is $ M $-projective. We prove that every …

R -PROJECTIVE MODULES OVER A SEMIPERFECT RING Page 1 Canad. Math. Bull. Vol. 24
(3), 1981 R -PROJECTIVE MODULES OVER A SEMIPERFECT RING BY RD KETKAR AND N …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

Introduction and Notation. A ring R is called a (von Neumann) regular ring if for each a in R
there exists an x in R such that a= axa. The notion of regularity has been extended to …

We introduce the class of “right almost V-rings” which is properly between the classes of
right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R …

Let R be a ring, na fixed nonnegative integer and F n the class of all left R-modules of flat
dimension at most n. A left R-module M is called n-copure projective if Ext R 1 (M, F)= 0 for …

Let R be a ring with identity and M a unital right R-module. Let Z*(M)={m epsilon M: mR<< E
(mR)}. In this study we consider the property (T): For every right R-module M with Z*(M) …

We say that a ring R is a right RDV-ring if each simple right R-module is RD-injective. In this
paper, we study the notion of RDV-rings which is a non-trivial generalization of V-rings and …