Lattice isomorphisms of alternative algebras
type: Item
instance of: scholarly article
title: Lattice isomorphisms of alternative algebras
zbMATH Open document ID: 0692.17012
DOI: 10.1016/0021-8693(90)90027-L
author: Jesús Laliena
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: This paper deals with the relation between finite dimensional alternative algebras A, B over a field which have isomorphic lattices of subalgebras, extending Barnes work on associative algebras [\textit{D. W. Barnes}, J. Aust. Math. Soc. 6, 106-121 (1966; Zbl 0141.031)]. One of the results says that B is semisimple if A is. Much of the work is (naturally, in view of Barnes paper) dedicated to the case that A is an eight- dimensional Cayley-Dickson algebra; special bases of such algebras are used in the proofs.
reviewed by: S Walcher
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 17A75
Mathematics Subject Classification ID: 06B99
zbMATH DE Number: 4132406
zbMATH Keywords: alternative algebras
zbMATH Keywords: isomorphic lattices of subalgebras
zbMATH Keywords: Cayley-Dickson algebra
MaRDI profile type: Publication
cites work: Q5665302
cites work: Nilpotent alternative algebras
cites work: Q5817043
cites work: On the radical of a ring with minimum condition
cites work: Lattice isomorphisms of associative algebras
cites work: Simple alternative rings
cites work: Alternative nil rings
cites work: Q5593040
cites work: Q3961610
cites work: On maximal subalgebras
cites work: Q5522244
cites work: The Open Case for Simple Alternative Rings
cites work: Alternative rings with d.c.c. I
cites work: Q3947798
description: scientific article; zbMATH DE number 4132406