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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Flexible algebras of degree two


Author: Joseph H. Mayne
Journal: Trans. Amer. Math. Soc. 172 (1972), 69-81
MSC: Primary 17A20
MathSciNet review: 0311727
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Abstract: All known examples of simple flexible power-associative algebras of degree two are either commutative or noncommutative Jordan. In this paper we construct an algebra which is partially stable but not commutative and not a noncommutative Jordan algebra. We then investigate the multiplicative structure of those algebras which are partially stable over an algebraically closed field of characteristic $ p \ne 2,3,5$. The results obtained are then used to develop conditions under which such algebras must be commutative.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0311727-1
Keywords: Flexible algebras, power-associative algebras, degree two, stable, noncommutative Jordan algebras
Article copyright: © Copyright 1972 American Mathematical Society