Generalizations of the primitive element theorem
type: Item
instance of: scholarly article
title: Generalizations of the primitive element theorem
zbMATH Open document ID: 0736.16008
DOI: 10.1155/S0161171291000637
author: Panagiotis Nikolopoulos
author: C. V. Nikolopoulos
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1992-06-26T00:00:00Z
full work available at URL: https://eudml.org/doc/46637
review text: The authors prove several ``primitive element type'' results for separable finitely generated (but not necessarily simple) algebras over infinite fields, and then extend these results to algebras over a commutative local or semilocal ring \(R\) where \(R/M\) is an infinite field for every maximal ideal \(M\). The main result of the paper is that a separable finitely generated algebra \(A\) over an infinite field \(F\) is generated by two elements, i.e. \(A=F[x,y]\) and if A is commutative, \(A=F[x]\).
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16S15
Mathematics Subject Classification ID: 12F10
zbMATH DE Number: 22383
zbMATH Keywords: primitive element
zbMATH Keywords: separable finitely generated algebra
zbMATH Keywords: generated by two elements
reviewed by: Margaret Beattie
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 22383