Nilpotent linear transformations and the solvability of power-associative nilalgebras

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2005-02-01
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Correa, Ivan
Julca, Pedro
Peresi, Luiz
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Hentzel, Irvin
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We prove some results about nilpotent linear transformations. As an application we solve some cases of Albert’s problem on the solvability of nilalgebras. More precisely, we prove the following results: commutative power-associative nilalgebras of dimension n and nilindex n − 1 or n − 2 are solvable; commutative power-associative nilalgebras of dimension 7 are solvable.

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This article is published as Correa, Ivan, Irvin Roy Hentzel, Pedro Pablo Julca, and Luiz Antonio Peresi. "Nilpotent linear transformations and the solvability of power-associative nilalgebras." Linear algebra and its applications 396 (2005): 35-53. doi:10.1016/j.laa.2004.08.007. Posted with permission.

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Thu Jan 01 00:00:00 UTC 2004
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