On nilpotency of generalized almost-jordan right-nilalgebras
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2008Metadata
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Arenas, Manuel
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On nilpotency of generalized almost-jordan right-nilalgebras
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We study the variety of algebras A over a field of characteristic ≠ 2, 3, 5 satisfying the identities xy=yx and β ((xx)y)x-((yx)x)x + γ ((xx)x)y-((yx)x)x=0, where β, γ are scalars. We do not assume power-associativity. We prove that if A admits a non-degenerate trace form, then A is a Jordan algebra. We also prove that if A is finite-dimensional and solvable, then it is nilpotent. We find three conditions, any of which implies that a finite-dimensional right-nilalgebra A is nilpotent. © 2008 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.
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URI: https://repositorio.uchile.cl/handle/2250/153811
DOI: 10.1142/S1005386708000072
ISSN: 10053867
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Algebra Colloquium, Volumen 15, Issue 1, 2018, Pages 69-82
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