-radical extensions of rings
Finite Rings with a Specified Group of Units.
Finitely generated projective modules and Fitting ideals.
First order calculi with values in right-universal bimodules
The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and Zumino [1990] and that in this language results are in a natural context, are easier to describe and handle. As a by-product we obtain intrinsic, coordinate-free and basis-independent generalization of the first order noncommutative differential calculi with partial derivatives.
-nilpotent units of commutative group rings
Suppose is a commutative unital ring and is an abelian group. We give a general criterion only in terms of and when all normalized units in the commutative group ring are -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].
Generalizations of morphic group rings.
Generalized Baer rings.
Generalized derivations and commutativity of rings with involution.
Generalized derivations on Lie ideals in prime rings
Let be a prime ring with its Utumi ring of quotients and extended centroid . Suppose that is a generalized derivation of and is a noncentral Lie ideal of such that for all , where is a fixed integer. Then one of the following holds:
Generalized periodic and generalized Boolean rings.
Generalized periodic rings.
Generalized primary rings and ideals.
Generators of large subgroups of the unit group of integral group rings.
Group algebras whose groups of normalized units have exponent 4
We give a full description of locally finite -groups such that the normalized group of units of the group algebra over a field of characteristic has exponent .
Group algebras with centrally metabelian unit groups.
Given a field K of characteristic p > 2 and a finite group G, necessary and sufficient conditions for the unit group U(KG) of the group algebra KG to be centrally metabelian are obtained. It is observed that U(KG) is centrally metabelian if and only if KG is Lie centrally metabelian.
Group rings with FC-nilpotent unit groups.
Let U(RG) be the unit group of the group ring RG. Groups G such that U(RG) is FC-nilpotent are determined, where R is the ring of integers Z or a field K of characteristic zero.
Group Rings with Units Torsion Over the Center.
-integral near-rings.
Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of ‘quantum’ type in all but a few exceptional cases.
Homomorphisms of group rings