Let R be a ring. We have studied rings whose projective modules have the extending
property of simple modules in [3] and [5]. In this note, we shall further study those rings when …

A module is serial if its submodules are linearly ordered with respect to inclusion. A ring R is
called left serial if RR is a direct sum of serial modules, and R is called serial if it is both left …

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 …

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 …

If M and N are right R-modules, M is called simple-N-injective if every R-homomorphism γ
from a submodule K of N into M with γ (K) simple extends to N. In this paper, a right R …

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 left module M over a ring R is cofaithful in case there is an embedding of R into a finite
product of copies of M. Our main result states that a semiprime ring R is left Goldie, that is …

F-rings need not be ∏-homogeneous Page 1 COMMUNICATIONS IN ALGEBRA, 17(6),
1495-1504 (1989) F-RINGS NEED NOT BE n-HOMOGENEOUS Gene D. Abrams University of …

Let R be a ring with identity 1. We denote the category of unital right (respectively left) R-
modules by 'U&m). MR will signify ME YJl&M E $ tJl). We will be concerned with certain …

In this paper modules with ascending chain condition (acc)(respectively, with descending
chain conditon (dcc)) on essential submodules are investigated: Finitely generated quasi …