Commutative Finitely Generated Algebras Satisfying ((yx)x)x = 0 are Solvable

Date
2009-01-01
Authors
Correa, Ivan
Hentzel, Irvin
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Mathematics
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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 yA. Our identify is then that Rx3 = 0.

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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.

Keywords
Commutative, solvable, nilpotent, finitely-generated
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