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 …

Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since
then, these classical artinian rings have continued to fascinate ring theorists with their …

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 …

Harada calls a ring $ R $ right simple-injective if every $ R $-homomorphism with simple
image from a right ideal of $ R $ to $ R $ is given by left multiplication by an element of $ R …

Abstract A right R–module E over a ring R is said to be maximally injective in case for any
maximal right ideal m of R, every R–homomorphism f: m→ E can be extended to an R …

We define a notion of generalized Jordan (resp. Lie) derivations and give some elementary
properties of generalized Jordan (resp. Lie) derivations. These categorical results …

R (finitely cogenerated) injective cogenerator in the category of right R-modules. The ring R
is a QF-ring if it is right PF and right (or left) artinian, and in this case R is two-sided PF and …

It is well known that a module M has finite length if and only if it is semi-artinian and
Noetherian or, equivalently, semi-noetherian and artinian. Our main result shows that finite …

There are three outstanding conjectures about quasi-Frobenius rings: The Faith conjecture
that every left perfect, right selfinjective ring is quasi-Frobenius; The FGF-conjecture that …