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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On algebras satisfying the identity $ (yx)x+x(xy)=2(xy)x$


Author: Robert A. Chaffer
Journal: Proc. Amer. Math. Soc. 31 (1972), 376-380
DOI: https://doi.org/10.1090/S0002-9939-1972-0288153-2
MathSciNet review: 0288153
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Abstract: Simple, strictly power-associative algebras satisfying the identity $ (yx)x + x(xy) = 2(xy)x$ over a field of characteristic not 2 or 3 have been classified by F. Kosier as commutative Jordan, quasi-associative, or of degree less than three. In the present paper those of degree three or greater are shown to be commutative, which eliminates the quasi-associative case mentioned above.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0288153-2
Keywords: Noncommutative Jordan algebra, flexible algebra, strictly power-associative, degree of an algebra, stable algebra
Article copyright: © Copyright 1972 American Mathematical Society