Extensions of nilpotent blocks.
Fair-sized projective modules
Filtrations, Stable Clifford Theory and Group-Graded Rings and Modules.
FP-injective and weakly quasi-Frobenius rings.
Frobenius n-group algebras
Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66-67).
-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].
G-algebras, Jacobson radical and almost split sequences.
Galois actions on rings and finite Galois coverings.
Galois generators and the subspace theorem.
Galois modules and embedding problems.
Generalizations of morphic group rings.
Generalized euclidean group rings.
Generating the augmentation ideal
Generators of large subgroups of the unit group of integral group rings.
Grothendieck ring of quantum double of finite groups
Let be a group algebra, and its quantum double. We first prove that the structure of the Grothendieck ring of can be induced from the Grothendieck ring of centralizers of representatives of conjugate classes of . As a special case, we then give an application to the group algebra , where is a field of characteristic and is a dihedral group of order .
Group algebras of abelian groups
Group Algebras of Finite Representation Type.
Group algebras of polynomial growth.
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.