This volume provides a comprehensive introduction to module theory and the related part of
ring theory, including original results as well as the most recent work. It is a useful and …

A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

This book surveys more than 125 years of aspects of associative algebras, especially ring
and module theory. It is the first to probe so extensively such a wealth of historical …

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 …

Let R be a commutative ring. The Gorenstein super finitely presented dimension of R is
defined as Gs. gl.\dim (R)=\sup {Gpd _ RM\,|\, M Gs. gl. dim (R)= sup Gpd RM| M is a super …

We study rings whose modules and module homomorphisms display behavior similar to that
of sets and their maps. For example, whenever there is an epimorphism A→ B, there is a …

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 …

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 …

Let R be a ring. The following results are proven. 1. If R is semilocal, right Kasch and right
simple-injective, then R is semiperfect, left and right finitely cogenerated. 2. If R is left perfect …

Let R be a ring. A left R-module M (resp. right R-module N) is called singly injective (resp.
singly flat) if Ext1 (F/C, M)= 0 (resp. Tor1 (N, F/C)= 0) for any cyclic submodule C of any …