Ring isomorphisms of \(H^*\)-algebras
type: Item
instance of: scholarly article
title: Ring isomorphisms of \(H^*\)-algebras
zbMATH Open document ID: 0892.46061
author: Armando R. Villena
author: Mohamed Zohry
published in: Journal of Algebra
publication date: 1996-07-09T00:00:00Z
review text: The authors prove that ring homomorphisms with dense image between complex infinite-dimensional topologically simple \(H^*\)-algebras are continuous. Moreover they are either linear or conjugate-linear isomorphisms. This result and another previous one by \textit{A. Rodríguez-Palacios} and \textit{J. A. Cuenca Mira} [J. Algebra 106, 1-14 (1987; Zbl 0616.46047)] allow a deep study of the ring isomorphisms between \(H^*\)-algebras with zero annihilator. More questions are treated, so the following assertions are proved: i) there are discontinuous ring isomorphisms between finite-dimensional topologically simple \(H^*\)-algebras; ii) ring isomorphisms between complex topologically simple \(H^*\)-algebras are \(\tau\)-linear for a suitable field automorphism \(\tau\) of \(\mathbb{C};\) iii) ring isomorphic complex associative \(H^*\)-algebras with zero annihilator are \(*\)-isomorphic.
reviewed by: José Antonio Cuenca Mira
Mathematics Subject Classification ID: 46H40
Mathematics Subject Classification ID: 46K70
Mathematics Subject Classification ID: 17A01
Mathematics Subject Classification ID: 46K15
zbMATH DE Number: 883763
zbMATH Keywords: \(H^*\)-algebra
zbMATH Keywords: ring isomorphism
zbMATH Keywords: continuity
MaRDI profile type: Publication
full work available at URL: jabr.1996.0123
OpenAlex ID: W2005834131
DOI: 10.1006/JABR.1996.0123
description: scientific article; zbMATH DE number 883763