Authors
Citation
Dz. Dokovic et Lg. Sweet, Infinite homogeneous algebras are anticommutative, P AM MATH S, 127(11), 1999, pp. 3169-3174
Citations number
11
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939
→ ACNP
Volume
127
Issue
11
Year of publication
1999
Pages
3169 - 3174
Database
ISI
SICI code
0002-9939(199911)127:11<3169:IHAAA>2.0.ZU;2-J
Abstract
A (non-associative) algebra A, over a field k, is called homogeneous if its
automorphism group permutes transitively the one dimensional subspaces of
A. Suppose A is a nontrivial finite dimensional homogeneous algebra over an
infinite field. Then we prove that x(2) = 0 for all x in A, and so xy = yx
for all x; y is an element of A.