Algebras which are nearly finite dimensional and their identities
type: Item
instance of: scholarly article
title: Algebras which are nearly finite dimensional and their identities
zbMATH Open document ID: 1006.16025
DOI: 10.1007/BF02784533
author: Daniel R. Farkas
author: Lance W. Small
published in: Israel Journal of Mathematics
publication date: 2002-12-10T00:00:00Z
review text: An infinite dimensional \(k\)-algebra \(R\) is called just infinite dimensional provided that every nonzero two-sided ideal has finite codimension in \(R\). The authors prove over an uncountable field \(k\) the following. If \(R\) is an affine, semiprimitive, just infinite dimensional \(k\)-algebra then either \(R\) is primitive or \(R\) satisfies a polynomial identity.
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 16P90
Mathematics Subject Classification ID: 16D60
zbMATH DE Number: 1786381
zbMATH Keywords: polynomial identities
zbMATH Keywords: Gelfand-Kirillov dimension
zbMATH Keywords: primitive algebras
zbMATH Keywords: semiprimitive algebras
zbMATH Keywords: just infinite dimensional algebras
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
cites work: Semisimple Representations and Affine Rings
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cites work: Q5577214
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cites work: Representations of the Gupta-Sidki group
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cites work: Prime affine algebras of Gelfand-Kirillov dimension one
cites work: Primitive algebras with arbitrary Gelfand-Kirillov dimension
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description: scientific article; zbMATH DE number 1786381