1. Introduction. Let R be a ring (associative and with identity). It is easy to see that every left
ideal of R is the (left) annihilator of a finite subset of R if and only if every cyclic left R-module …

It is well known that if R is a ring such that each right R-module Ž. embeds in a free module,
then R is a quasi-Frobenius QF ring. However, if the embedding is restricted to finitely …

A ring R is called left FGF (resp. CF) if every finitely generated (resp. cyclic) left R-module
embeds in a free module. In this paper we give new partial affirmative answers to two open …

Because F is a free module of infinite rank we see that F^ Fn all n^ l. It follows that H^ Hn as
right (or left) H-modul es. So H is isomorphic (as ring) to Hn, forali n> 1. Further every finitely …

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 …

In this paper we are mainly concerned with rings satisfying the descending chain condition
(dcc) on left principal ideals. Such rings are called left coperfect rings in this paper. When left …

Let (F, A) and (G, B) be vector spaces over division rings F and G, and E (F, A) and E (G, B)
the corresponding endomorphism rings. Baer in [2] showed that E (F, A) and E (G, B) are anti …

In § 1, we begin with a basic theorem which describes a convenient embedding of a
nonsingular left R-module into a complete direct product of copies of the left injective hull of …

The purpose of this paper is to characterize quasi-Frobenius, QF, rings in terms of
relationships assumed to exist for each cyclic or finitely generated left module between the …

Self-injective rings and endomorphisms of free modules Page 1 SELF-INJECTIVE RINGS OF
FREE MODULES VI Gemintern AND ENDOMORPHISMS UDC 512.4 It is shown that the ring of …