Article
Commutative Finitely Generated Algebras Satisfying ((yx)x)x = 0 are Solvable
Rocky Mountain Journal of Mathematics
Document Type
Article
Disciplines
- Algebra and
- Mathematics
Publication Version
Published Version
Publication Date
1-1-2009
DOI
10.1216/RMJ-2009-39-3-757
Abstract
We study commutative, nonassociative algebras satisfying the identity
(1) ((yx)x)x = 0
We show that finitely generated algebras over a field K of characteristic ≠ 2 satisfying (1) are solvable. For x in an algebra A, define the multiplicatin operator Rx by yRx = yx, for all y ∈ A. Our identify is then that Rx3 = 0.
Copyright Owner
Rocky Mountain Mathematics Consortium
Copyright Date
2009
Language
en
File Format
application/pdf
Citation Information
Ivan Correa and Irvin R. Hentzel. "Commutative Finitely Generated Algebras Satisfying ((yx)x)x = 0 are Solvable" Rocky Mountain Journal of Mathematics Vol. 39 Iss. 3 (2009) p. 757 - 764 Available at: http://works.bepress.com/irvin-hentzel/8/
This article is published as Correa, Ivan, and Irvin Roy Hentzel. "Commutative Finitely Generated Algebras Satisfying ((yx) x) x= 0 are Solvable." Rocky Mountain Journal of Mathematics 39, no. 3 (2009): 757-764. DOI: 10.1216/RMJ-2009-39-3-757. Posted with permission.