Separable algebras over infinite fields are 2-generated and finitely presented.
type: Item
instance of: scholarly article
title: Separable algebras over infinite fields are 2-generated and finitely presented.
zbMATH Open document ID: 1190.16026
author: Marcin Mazur
author: Bogdan V. Petrenko
published in: Archiv der Mathematik
publication date: 2010-01-08T00:00:00Z
review text: It is proved that a separable algebra over an infinite field \(K\) admits a finite presentation by two generators. This follows by the fact that the number of generators is invariant under field extension. As an application, the classification of two-dimensional simple \(K\langle x,y\rangle\)-modules [see \textit{H. Kraft}, in Representations of algebras, 3rd int. Conf., Puebla/Mex. 1980, Lect. Notes Math. 944, 180-258 (1982; Zbl 0517.14016)] is considered over a commutative ring.
reviewed by: Wolfgang Rump
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 16S15
Mathematics Subject Classification ID: 16R30
zbMATH DE Number: 5655337
zbMATH Keywords: separable algebras
zbMATH Keywords: generators of algebras
zbMATH Keywords: presentations of algebras
zbMATH Keywords: conjugacy invariants
MaRDI profile type: Publication
full work available at URL: s00013-009-0058-8
OpenAlex ID: W1983306381
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DOI: 10.1007/S00013-009-0058-8
description: scientific article; zbMATH DE number 5655337