Radical properties of perfect modules.
Rad-supplemented modules
Regularly weakly based modules over right perfect rings and Dedekind domains
A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains.
Rings of Quotients of Perfect Rings.
Rings satisfying certain chain conditions.
Rings whose Elements are Quasi-Regular or Regular
Rings whose proper factors are right perfect
We show that practically all the properties of almost perfect rings, proved by Bazzoni and Salce [Colloq. Math. 95 (2003)] for commutative rings, also hold in the non-commutative setting.
Rings with indecomposable modules local.
Ring-theoretic properties of Iwasawa algebras: a survey.
Semi-perfect and F-semi-perfect modules.
Semi-Perfect q-Rings.
Smash products, group actions and group graded rings.
Some chain conditions on weak incidence algebras.
Some results on quasi-Frobenius rings
We give some new characterizations of quasi-Frobenius rings by the generalized injectivity of rings. Some characterizations give affirmative answers to some open questions about quasi-Frobenius rings; and some characterizations improve some results on quasi-Frobenius rings.
Sur un Théorème de Green.
The classification of compact right chain rings.
The coefficient ring of the skew group ring
The lattice R-tors for perfect rings.
Topologically semiperfect rings
Towards a theory of Bass numbers with application to Gorenstein algebras
The notion of Gorenstein rings in the commutative ring theory is generalized to that of Noetherian algebras which are not necessarily commutative. We faithfully follow in the steps of the commutative case: Gorenstein algebras will be defined using the notion of Cousin complexes developed by R. Y. Sharp [Sh1]. One of the goals of the present paper is the characterization of Gorenstein algebras in terms of Bass numbers. The commutative theory of Bass numbers turns out to carry over with no extra changes....