Examples in finite Gel'fand-Kirillov dimension
type: Item
instance of: scholarly article
title: Examples in finite Gel'fand-Kirillov dimension
zbMATH Open document ID: 1028.16012
DOI: 10.1016/S0021-8693(03)00021-8
author: Jason P. Bell
published in: Journal of Algebra
publication date: 2003-06-09T00:00:00Z
review text: The author modifies constructions of \textit{K. I. Beidar} [Usp. Mat. Nauk 36, No. 6(222), 203-204 (1981; Zbl 0482.16008)] and L. Small and proves that for countably generated prime \(F\)-algebras of finite GK-dimension there exists an affinization having finite GK-dimension. Using this result, the author constructs the following examples. (1) For any field there exists a prime affine algebra of GK-dimension two that is neither primitive nor PI. (2) For any countable field \(F\) there exists a prime affine \(F\)-algebra of GK-dimension three that has non-nil Jacobson radical. (3) For any countable field \(F\) there exists an affine primitive \(F\)-algebra of GK-dimension at most four with center equal to a polynomial ring. (4) For a countable field \(F\) there exists a primitive affine Jacobson \(F\)-algebra of GK-dimension three that does not satisfy the Nullstellensatz.
Mathematics Subject Classification ID: 16P90
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16N20
Mathematics Subject Classification ID: 16R10
zbMATH DE Number: 1924687
zbMATH Keywords: Gelfand-Kirillov dimension
zbMATH Keywords: prime algebras
zbMATH Keywords: affine algebras
zbMATH Keywords: Jacobson radical
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1924687