300 AFXENDARIZ in one case that the radical is finitely generated and nilpotent and in the
other that the left socle is finitely generated. This is the essence of section 2; the first section …

A classical result of Zelinsky states that every linear transformation on a vector space V,
except when V is one-dimensional over ℤ2, is a sum of two invertible linear transformations …

Abstract A right R-module M is said to be finendo provided that as a left module over its
endomorphism ring it is finitely generated. Let B= End MR. Then B n→ M→ 0 is exact for …

Note that, if X is a subset of a ring R, l (X)(resp. r (X)) is just the left (resp. right) annihilator of
X in R since(RR)*= RR. We call a ring R right PF if every faithful right R-module is a …

This paper was motivated by one of Armendariz and Park [I] in which it is proved that a left
self-injective ring R is quasi-Frobenius (QF) if the factor ring of R modulo its left (or right) …

Following H. Bass[3, p. 476], we call A torsionless if ƒÂA is a monomorphism and reflexive if
ƒÂA is an isomorphism. If X is a subset of A (resp. A*) we denote its annihilator in A*(resp. A) …

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 …

Lntroduction It is easily seen that if an R-module is a generator in the category mod-R, then it
is faithful. However, the converse is not necessarily true. Naturally one is led to ask for which …

Let R be a ring with an identity. A ring R will be called a left (right) q*-ring if every R-
homomorphic image of R as a left (right) R-module is quasi-projective, that is, if every cyclic …