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.
Remarks on injectivity
Representation-finite selfinjective algebras of class
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.
Rings with zero intersection property on annihilators: Zip rings.
Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent:(ZIP 1) If the right anihilator X⊥ of a subset X of R is zero, then X1⊥ = 0 for a finite subset X1 ⊆ X.(ZIP 2) If L is a left ideal and if L⊥ = 0, then L1⊥ = 0 for a finitely generated left ideal L1 ⊆ L.In [12], Zelmanowitz noted that any ring R satisfying the d.c.c. on anihilator right ideals (= dcc ⊥) is a right zip ring, and hence, so is any subring of R. He...
Ring-theoretic properties of Iwasawa algebras: a survey.