We say that a ring K is (right) split by a subring A provided that A is an (right) A-module direct
summand of K. Then K is said to be a split extension of A. By a theorem of Azumaya [lJ, a …

A ring R is right finitely pseudo Frobenius (FPF) if every finitely generated faithful right jR-
module generates the category of right jR-modules. In [2], C. Faith has shown that a …

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 …

A ring R is called right FP-injective if every R-homomor-phism from a finitely generated
submodule of a free right R-module F into R extends to F. In this paper a ring R will be called …

ON SEMIPERFECT FPF-RINGS Page 1 Canad. Math. Bull. Vol. 37 (2), 1994 pp. 287-288 ON
SEMIPERFECT FPF-RINGS MOHAMED YOUSIF ABSTRACT. We show that a semiperfect right …

A ring is quasi-Frobenius if and only if every injective right R-module is projective. Thus, the
ring has the property that each right-module embeds in a free module if and only if the ring is …

(right) PF-rings. This class of rings and another related generalization of quasi-Frobenius
rings, the (two-sided) cogenerator rings, have been studied recently by a number of authors …

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 …

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 …

NOTES ON FP-PROJECTIVE MODULES AND FP-INJECTIVE MODULES 1. Introduction
Throughout this paper, all rings are associative with id Page 1 February 17, 2006 17:49 …