Topic
Generic polynomial
About: Generic polynomial is a research topic. Over the lifetime, 608 publications have been published within this topic receiving 6784 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors construct a small category whose objects are monic square-free polynomials with coefficients in a field F, and prove that for a monic, irreducible, and normal polynomial, Aut ( f ) is the usual Galois group of f.
2 citations
DOI•
01 May 2009TL;DR: In this article, it was shown that there exist subgroups K and N of G such that K is a normal subgroup of N and one of the following three cases holds: (i) VB(B K ) is a central Galois algebra over C with Galois group K, (ii) V B K )i s separable C-algebra with an automorphism group induced by and isomorphic with K.
Abstract: Let B be a Hirata separable and Galois extension of B G with Galois group G of order n invertible in B for some integer n, C the center of B, and VB(B G ) the commutator subring of B G in B. It is shown that there exist subgroups K and N of G such that K is a normal subgroup of N and one of the following three cases holds: (i) VB(B K ) is a central Galois algebra over C with Galois group K, (ii) VB(B K )i s separable C-algebra with an automorphism group induced by and isomorphic with K, and (iii) B K is a central algebra over VB(B K ) and a Hirata separable Galois extension of B N with Galois group N/K. More characterizations for a central Galois algebra VB(B K ) are given.
2 citations
2 citations
TL;DR: In this article, a proper polynomial map of arbitrary topological degree up to equivalence was investigated. But the results were restricted to the case where the maps are Galois coverings.
Abstract: Two proper polynomial maps $f_1, f_2 \colon \mathbb{C}^2 \longrightarrow
\mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi_1, \Phi_2 \in \textrm{Aut}(\mathbb{C}^2)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$.
We investigate proper polynomial maps of arbitrary topological degree $d \geq 2$ up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lamy in the case $d=2$.
2 citations
TL;DR: In this paper, the authors construct idempotent 2-cocycles of a finite Galois field extension with Galois group G, where G is a partition of G to A f and A f is the associated weak crossed product K-algebra.
2 citations