The Functional Equation. (Short Communication).
The Functor Bext under the Negation of CH.
The fundamental group of a Galois cover of .
The fundamental groups of subsets of closed surfaces inject into their first shape groups.
The fundamental representation of a completely regular semigroup.
The fundamental representation of a regular semigroup.
The fundamental theorem for the projective line over commutative rings. (Short Communication).
The fundamental theorem for the projective line over commutative rings.
The fundamental theorem of prehomogeneous vector spaces modulo (With an appendix by F. Sato)
For a number field with ring of integers , we prove an analogue over finite rings of the form of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where is a big enough prime ideal of and . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [Character sums associated to prehomogeneous vector spaces, Compos. Math., 113(1998), 237–346] to the functional equation of -functions...
The Galois correspondence between subvariety lattices and monoids of hpersubstitutions
Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.
The Galois sturcture of the square root of the inverse different.
The garden of quantum spheres
A list of known quantum spheres of dimension one, two and three is presented.
The Garnir relations for Weyl groups of type .
The generalized commutativity degree in a finite group.
The generalized criterion of Dieudonné for primary valuated groups
The generalized criterion of Dieudonné for valuated -groups
We prove that if is an abelian -group with a nice subgroup so that is a -group, then is a -group if and only if is a -subgroup in provided that is equipped with a valuation induced by the restricted height function on . In particular, if in addition is pure in , is a -group precisely when is a -group. This extends the classical Dieudonné criterion (Portugal. Math., 1952) as well as it supplies our recent results in (Arch. Math. Brno, 2005), (Bull. Math. Soc. Sc. Math....
The generalized translational hull of a semigroup.
The genus problem for one-relator products of locally indicable groups.
The geometric invariants of direct products of virtually free groups.
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...