On some minimal supervarieties of exponential growth.
type: Item
instance of: scholarly article
title: On some minimal supervarieties of exponential growth.
zbMATH Open document ID: 1279.16021
author: Ernesto Spinelli
author: M. Onofrio Di Vincenzo
published in: Journal of Algebra
publication date: 2013-04-17T00:00:00Z
review text: Let \(F\) be a field of characteristic \(0\), a variety of (associative) PI superalgebras over \(F\) is minimal of superexponent \(d\) if its exponent equals \(d\) and each proper subvariety is of superexponent \(<d\). Recall that the exponent is the limit (\(m\to\infty\)) of the \(m\)-th root of the \(m\)-th codimension. The main result of the paper under review states that every minimal variety of superalgebras of finite basic rank is generated by an algebra of a concrete list, called minimal superalgebras. On the other hand it is proved that if \(A\) is a minimal superalgebra whose semisimple part decomposes as a direct sum of graded simple components that are simple, then \(A\) generates a minimal supervariety. The same is shown to be true when the semisimple part of \(A\) consists of exactly two graded simple components.
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16W55
Mathematics Subject Classification ID: 16R10
zbMATH DE Number: 6154885
zbMATH Keywords: superalgebras
zbMATH Keywords: polynomial identities
zbMATH Keywords: superexponents
zbMATH Keywords: supercodimension sequences
zbMATH Keywords: minimal supervarieties
zbMATH Keywords: graded simple components
reviewed by: Plamen Koshlukov
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2012.07.005
OpenAlex ID: W1985692289
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DOI: 10.1016/J.JALGEBRA.2012.07.005
description: scientific article; zbMATH DE number 6154885