The centre of completed group algebras of pro- groups.
The characteristic variety of a generic foliation
We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.
The coefficient ring of the skew group ring
The construction of -solvable Abelian groups
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 duality theorem for twisted smash products of Hopf algebras and its applications
Let denote the twisted smash product of an arbitrary algebra A and a Hopf algebra H over a field. We present an analogue of the celebrated Blattner-Montgomery duality theorem for , and as an application we establish the relationship between the homological dimensions of and A if H and its dual H* are both semisimple.
The Endomorphism Ring Theorem for Frobenius Extensions.
The Equivalence of Various Generalizations of Group Rings and Modules.
The existence of Galois sets
The existence of identity of orthodox semigroup rings.
The finite dimension property of the irreducible representations of Noetherian -Lie algebras.
The free -ring is a graded -ring.
The -graded identities of the Grassmann Algebra
Let be a finite abelian group with identity element and be an infinite dimensional -homogeneous vector space over a field of characteristic . Let be the Grassmann algebra generated by . It follows that is a -graded algebra. Let be odd, then we prove that in order to describe any ideal of -graded identities of it is sufficient to deal with -grading, where , and if . In the same spirit of the case odd, if is even it is sufficient to study only those -gradings such that...
The Galois algebras and the Azumaya Galois extensions.
The Galois extensions induced by idempotents in a Galois algebra.
The Gelfand-Kirillov dimension of rings with Hopf algebra action.
The general Ikehata theorem for -separable crossed products.
The general structure of inverse polynomial modules
In this paper we compute injective, projective and flat dimensions of inverse polynomial modules as -modules. We also generalize Hom and Ext functors of inverse polynomial modules to any submonoid but we show Tor functor of inverse polynomial modules can be generalized only for a symmetric submonoid.
The global homological dimension of semi-trival extensions of rings.