The Frobenius theorem on -dimensional quantum hyperplane.
The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules
We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category . More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke’s theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.
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 Galois module structure of algebraic integer rings in fields with generalised quaternion group
The Gelfand-Kirillov Dimension of a Tensor Product.
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 geometric reductivity of the quantum group
We introduce the concept of geometrically reductive quantum group which is a generalization of the Mumford definition of geometrically reductive algebraic group. We prove that if G is a geometrically reductive quantum group and acts rationally on a commutative and finitely generated algebra A, then the algebra of invariants is finitely generated. We also prove that in characteristic 0 a quantum group G is geometrically reductive if and only if every rational G-module is semisimple, and that in...
The Geometry of Representations of Am .
The global basie dimension of artin rings [Book]
The global homological dimension of semi-trival extensions of rings.
The Global Homological Dimension of Some Algebras of Differential Operators.
The Grothendieck group of G-equivariant modules over coordinate rings of G-orbits
The Grothendieck ring of quantum double of quaternion group
Let be an algebraically closed field of characteristic , and let be the quaternion group. We describe the structures of all simple modules over the quantum double of group algebra . Moreover, we investigate the tensor product decomposition rules of all simple -modules. Finally, we describe the Grothendieck ring by generators with relations.
The group of automorphisms of a commutative algebra.
The group of automorphisms of the coordinate ring of quantum symplectic space.
The Heart of Prime Ideals in Ore Extensions.