On a class of free Galois extensions.
On Azumaya Galois extensions and skew group rings.
On central commutator Galois extensions of rings.
On certain classes of Galois extensions of rings.
On characterizations of a center Galois extension.
On commutative twisted group rings
Let be an abelian group, a commutative ring of prime characteristic with identity and a commutative twisted group ring of over . Suppose is a fixed prime, and are the -components of and of the unit group of , respectively. Let be the multiplicative group of and let be the -th Ulm-Kaplansky invariant of where is any ordinal. In the paper the invariants , , are calculated, provided . Further, a commutative ring with identity of prime characteristic is said...
On faithful projective representations of finite abelian p-groups over a field of characteristic p
Let G be a noncyclic abelian p-group and K be an infinite field of finite characteristic p. For every 2-cocycle λ ∈ Z²(G,K*) such that the twisted group algebra is of infinite representation type, we find natural numbers d for which G has infinitely many faithful absolutely indecomposable λ-representations over K of dimension d.
On Flatness and Projectivity of a Ring as a Module over a Fixed Subring.
On -separable and Galois extensions of rings.
On indecomposable projective representations of finite groups over fields of characteristic p > 0
Let G be a finite group, F a field of characteristic p with p||G|, and the twisted group algebra of the group G and the field F with a 2-cocycle λ ∈ Z²(G,F*). We give necessary and sufficient conditions for to be of finite representation type. We also introduce the concept of projective F-representation type for the group G (finite, infinite, mixed) and we exhibit finite groups of each type.
On intecomposable Lattices over Twisted group rings
On local weak crossed product orders
Let Λ = (S/R,α) be a local weak crossed product order in the crossed product algebra A = (L/K,α) with integral cocycle, and the inertial group of α, for S* the group of units of S. We give a condition for the first ramification group of L/K to be a subgroup of H. Moreover we describe the Jacobson radical of Λ without restriction on the ramification of L/K.
On modular projective representations of finite nilpotent groups
Our aim is to determine necessary and sufficient conditions for a finite nilpotent group to have a faithful irreducible projective representation over a field of characteristic p ≥ 0.
On Separable Subalgebras of Azumaya Algebras
On several varieties of cacti and their relations.
On Splitting Rings for Azumaya Skew Group Rings
On the Jacobson radical of graded rings.
On twisted group algebras of OTP representation type
Assume that S is a commutative complete discrete valuation domain of characteristic p, S* is the unit group of S and is a finite group, where is a p-group and B is a p’-group. Denote by the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). We give necessary and sufficient conditions for to be of OTP representation type, in the sense that every indecomposable -module is isomorphic to the outer tensor product V W of an indecomposable -module V and an irreducible -module...
On weak center Galois extensions of rings.
Représentations de dimension finie de l’algèbre de Cherednik rationnelle
On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.