Primitive superalgebras with superinvolution
type: Item
instance of: scholarly article
title: Primitive superalgebras with superinvolution
zbMATH Open document ID: 0915.16036
published in: Journal of Algebra
publication date: 1999-04-13T00:00:00Z
review text: The author studies primitive associative superalgebras and develops their structure theory in the spirit of classical structure theory of (ordinary) associative algebras. In particular, he proves a superanalogue of the density theorem, gives a description of the artinian simple superrings as algebras of endomorphisms of a finite dimensional superspace over a division superalgebra and determines the isomorphisms between two artinian simple superrings. He also presents a complete list of central division superalgebras over a field in terms of the (ordinary) central division algebras over the same field. Then the author describes the primitive superrings with a minimal right superideal. An important application is for the case when the primitive superring has a superinvolution which is crucial for the study of finite dimensional central simple Jordan algebras. Another application is the description of simple superrings with superinvolution.
Mathematics Subject Classification ID: 16W55
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 17C70
zbMATH DE Number: 1213836
zbMATH Keywords: associative superalgebras
zbMATH Keywords: primitive superalgebras
zbMATH Keywords: division superalgebras
zbMATH Keywords: Artinian superalgebras
zbMATH Keywords: superinvolutions
zbMATH Keywords: density theorem
zbMATH Keywords: simple superrings
zbMATH Keywords: primitive superrings
zbMATH Keywords: central simple Jordan algebras
author: Michel L. Racine
reviewed by: Vesselin Drensky
MaRDI profile type: Publication
full work available at URL: jabr.1997.7412
OpenAlex ID: W2032205557
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DOI: 10.1006/JABR.1997.7412
description: scientific article; zbMATH DE number 1213836