One of the main results of this paper is the characterization of left FP-injective rings as rings
over which every finitely presented right module is torsionless. The necessity of the …

Motivated by a result of Mochizuki [Mochizuki, H.(1965). Finitistic global dimension for rings.
Pacific J. Math. 15 (1): 249–258] that, for a left perfect ring R with Jacobson radical if and …

Theorems of Osofsky and Kato imply that a right and left self-injective one-sided perfect ring
is quasi-Frobenius (= QF). The corresponding question for one-sided self-injective one or …

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A
left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1 (G, M)= 0 …

We shall call a ring R a left IF ring if every injective left R-module is flat. The purpose of this
paper is to characterize left and two-sided IF rings in several ways and to give some …

Harada calls a ring $ R $ right simple-injective if every $ R $-homomorphism with simple
image from a right ideal of $ R $ to $ R $ is given by left multiplication by an element of $ R …

Quasi-frobenius (= QF) rings have many interesting characterizations. One such, due to
Ikeda [17] is that these rings are right (left) artinian and right (left) self-injective. Thus, if R is …

We show that ifRis a semiperfect ring with essential left socle andrl (K)= Kfor every small
right idealKofR, thenRis right continuous. Accordingly some well-known classes of rings …

A ring R is called right weakly continuous if the right annihilator of each element is essential
in a summand of R, and R satisfies the right C2-condition (every right ideal that is isomorphic …

The concept of weak relative-injectivity of modules was introduced originally in [10], where it
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …