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For a number field $K$ with ring of integers $𝒪_{K}$ , we prove an analogue over finite rings of the form $𝒪_{K} / 𝒫^{m}$ of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where $𝒫$ is a big enough prime ideal of $𝒪_{K}$ and $m > 1$ . 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 $L$ -functions...

The Galois correspondence between subvariety lattices and monoids of hpersubstitutions

Klaus Denecke, Jennifer Hyndman, Shelly L. Wismath (2000)

Discussiones Mathematicae - General Algebra and Applications

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.

B. Erez (1991)

Mathematische Zeitschrift

The garden of quantum spheres

Ludwik Dąbrowski (2003)

Banach Center Publications

A list of known quantum spheres of dimension one, two and three is presented.

The Garnir relations for Weyl groups of type $C_{n}$ .

Can, Himmet (2008)

The Electronic Journal of Combinatorics [electronic only]

The generalized commutativity degree in a finite group.

Russo, Francesco (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

The generalized criterion of Dieudonné for primary valuated groups

Peter Vassilev Danchev (2007)

Acta Mathematica Universitatis Ostraviensis

The generalized criterion of Dieudonné for valuated $p$ -groups

Peter Vassilev Danchev (2006)

Acta Mathematica Universitatis Ostraviensis

We prove that if $G$ is an abelian $p$ -group with a nice subgroup $A$ so that $G / A$ is a $Σ$ -group, then $G$ is a $Σ$ -group if and only if $A$ is a $Σ$ -subgroup in $G$ provided that $A$ is equipped with a valuation induced by the restricted height function on $G$ . In particular, if in addition $A$ is pure in $G$ , $G$ is a $Σ$ -group precisely when $A$ is a $Σ$ -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....

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The functional equation f(xy) = ff(x) xy ff(y) in a partially ordered monoid.

The Functional Equation. (Short Communication).

The Functor Bext under the Negation of CH.

The fundamental group of a Galois cover of $ℂ ℙ^{1} \times T$ .

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 $p^{m}$ (With an appendix by F. Sato)