Tame and Galois extensions with respect to Hopf orders.
Tame orders
Tame tensor products of algebras
With the help of Galois coverings, we describe the tame tensor products of basic, connected, nonsimple, finite-dimensional algebras A and B over an algebraically closed field K. In particular, the description of all tame group algebras AG of finite groups G over finite-dimensional algebras A is completed.
The adjoint representation of group algebras and enveloping algebras.
In this paper we study the Hopf adjoint action of group algebras and enveloping algebras. We are particularly concerned with determining when these representations are faithful. Delta methods allow us to reduce the problem to certain better behaved subalgebras. Nevertheless, the problem remains open in the finite group and finite-dimensional Lie algebra cases.
The Auslander-Reiten quiver of a modular group algebra revisited.
The Bass conjecture and growth in groups
We discuss Bass's conjecture on the vanishing of the Hattori-Stallings rank from the viewpoint of geometric group theory. It is noted that groups without u-elements satisfy this conjecture. This leads in particular to a simple proof of the conjecture in the case of groups of subexponential growth.
The centre of completed group algebras of pro- groups.
The coefficient ring of the skew group ring
The converse of Schur's Lemma in group rings
In this paper, we study the structure of group rings by means of endomorphism rings of their modules. The main tools used here, are the subrings fixed by automorphisms and the converse of Schur's lemma. Some results are obtained on fixed subrings and on primary decomposition of group rings.
The cyclic homology of the group rings.
The Equivalence of Various Generalizations of Group Rings and Modules.
The Heart of Prime Ideals in Ore Extensions.
The Indecomposable Modular Representations of Certain Groups with Dihedral Sylow Subgroup.
The isomorphic description of torsion units in commutative group rings over fields with positive characteristic.
The maximal quotient rings of regular group rings (III).
We give a new proof of the main result of [1] which does not use the classification of the finite simple groups.
The number of indecomposable Schur rings over a cyclic 2-group.
The parametrization of interior algebras.
The rank of G0 for polycyclic group algebras
The Schur Subgroup of a Real Cyclotomic Field.
The special circulant matrix and units in group rings.