Rings with a finite set of nonnilpotents.
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.
Selfinjective algebras of polynomial growth.
Selfinjective and Simply Connected Algebras.
Skew inverse power series rings over a ring with projective socle
A ring is called a right -ring if its socle, , is projective. Nicholson and Watters have shown that if is a right -ring, then so are the polynomial ring and power series ring . In this paper, it is proved that, under suitable conditions, if has a (flat) projective socle, then so does the skew inverse power series ring and the skew polynomial ring , where is an associative ring equipped with an automorphism and an -derivation . Our results extend and unify many existing results....
Skew polynomial extensions over zip rings.
Skew polynomial rings satisfying - property.
Some chain conditions on weak incidence algebras.
Some characterizations of tilted algebras.
Some conditions for finiteness and commutativity of rings.
Some conditions for finiteness of a ring.
Some examples of nil Lie algebras
Generalizing Petrogradsky’s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand–Kirillov dimension over any field of positive characteristic.
Some external characterizations of SV-rings and hereditary rings.
Some results on -injective modules, -flat modules and -coherent rings
Let be two non-negative integers. A left -module is called -injective, if for every -presented left -module . A right -module is called -flat, if for every -presented left -module . A left -module is called weakly --injective, if for every -presented left -module . A right -module is called weakly -flat, if for every -presented left -module . In this paper, we give some characterizations and properties of -injective modules and -flat modules in the cases...
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.
Some Results on Rings with Chain Conditions.
Some small-centralizer properties for rings.
Spectral radius and seminorms in finite-dimensional algebras. II