ABSOLUTE-VALUED ALGEBRAIC ALGEBRAS ARE FINITE-DIMENSIONAL

Authors
ELAMIN K RAMIREZ MI PALACIOS AR
Citation
K. Elamin et al., ABSOLUTE-VALUED ALGEBRAIC ALGEBRAS ARE FINITE-DIMENSIONAL, Journal of algebra, 195(1), 1997, pp. 295-307
Citations number
34
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Journal of algebra → ACNP
ISSN journal
00218693
Volume
195
Issue
1
Year of publication
1997
Pages
295 - 307
Database
ISI
SICI code
0021-8693(1997)195:1<295:AAAAF>2.0.ZU;2-A
Abstract
We prove that if A is a non-associative algebra over the field of real numbers, if there is a norm parallel to.parallel to on A satisfying p arallel to xy parallel to = parallel to x parallel to parallel to y pa rallel to for all x, y in A, and if every one-generated subalgebra of A is finite-dimensional, then A is finite-dimensional. (C) 1997 Academ ic Press.