Jordan ideals revisited.
type: Item
instance of: scholarly article
title: Jordan ideals revisited.
zbMATH Open document ID: 1079.16016
author: Ajda Fošner
author: Maja Fošner
author: Matej Brešar
published in: Monatshefte für Mathematik
publication date: 2005-06-14T00:00:00Z
review text: The authors approach the study of Jordan ideals in rings by using the identity \([[a,b],c]=a\circ(b\circ c)-b\circ(a\circ c)\). This provides a fairly simple way to recapture the classical results that relate Jordan ideals to ideals. The approach here puts these known results is a more general setting applicable to certain rings of operators. The authors' methods exend to graded algebras with an anti-symmetric bicharacter, giving Jordan color algebras. Here they obtain recent results on \(\varepsilon\)-Jordan ideals, analogous to the results in the classical case, but again in a more general setting. When the rings, graded or not, have involution, then the authors recover known results on the Jordan ideals of the set of symmetric elements.
reviewed by: Charles Lanski
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 17C50
Mathematics Subject Classification ID: 46H10
Mathematics Subject Classification ID: 17C20
zbMATH DE Number: 2175899
zbMATH Keywords: Jordan ideals
zbMATH Keywords: symmetric elements
zbMATH Keywords: graded algebras
zbMATH Keywords: rings of operators
zbMATH Keywords: Jordan color algebras
zbMATH Keywords: rings with involution
MaRDI profile type: Publication
full work available at URL: s00605-004-0279-7
OpenAlex ID: W2048179569
DOI: 10.1007/S00605-004-0279-7
description: scientific article; zbMATH DE number 2175899