Year: 2016
Type: article
Abstract: The genus gen( D ) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [ D ′] ∈ Br( F ), where D ′ is a central division F-algebra having the same maximal subfields as D . For any prime p , we construct a division algebra of degree p with infinite genus. Moreover, we show that there exists a field K such that there are infinitely many nonisomorphic central division K -algebras of degree p and any two such algebras have the same genus.
Author: Sergey V. Tikhonov
Institution: Belarusian State University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2591761857