Special Quasi-triads and Integral Group Rings of Finite Representation Type, II

On Torsion Subgroups in Integral Group Rings of Finite Groups

Central Units in Integral Group Rings II 1

Recent work on central units of integral group rings is surveyed. In particular we present two methods of constructing central units, induction and lifting, and demonstrate how these constructions can often be used to find generators for large subgroups in the full group of central units of an integral group ring.

Quasi-Complete Primary Components in Modular Abelian Group Rings over Special Rings

Let G be a multiplicatively written p-separable abelian group and R a commutative unitary ring of prime characteristic p so that Rp i has nilpotent elements for each positive integer i > 1. Then, we prove that, the normed unit p-subgroup S(RG) of the group ring RG is quasi-complete if and only if G is a bounded p-group. This strengthens our recent results in (Internat. J. Math. Analysis, 2006) ...

Rational Group Algebras of Finite Groups: from Idempotents to Units of Integral Group Rings

We give an explicit and character-free construction of a complete set of orthogonal primitive idempotents of a rational group algebra of a finite nilpotent group and a full description of the Wedderburn decomposition of such algebras. An immediate consequence is a well-known result of Roquette on the Schur indices of the simple components of group algebras of finite nilpotent groups. As an appl...

D-modules over Rings with Finite F-representation Type

Smith and Van den Bergh [29] introduced the notion of finite F-representation type as a characteristic p analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite F-representation type. The first property states that if R = L n≥0 Rn is a Noetherian graded ring with finite (graded) F-representation type, then for every non-zerodi...