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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Scalar dependent algebras
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by Raymond Coughlin, Erwin Kleinfeld and Michael Rich PDF
Proc. Amer. Math. Soc. 39 (1973), 69-72 Request permission

Abstract:

An algebra $A$ over a field $F$ will be called scalar dependent in case for every $x,y,z$ in $A$ there exists a function $g(x,y,z)$ in $F$ such that $(xy)z = g(x,y,z)x(yz)$. The main result of this paper is that any scalar dependent algebra which contains a nonzero idempotent must always be associative. Since there are known to exist scalar dependent algebras which are not associative, the hypothesis regarding the existence of an idempotent is actually necessary.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 39 (1973), 69-72
  • MSC: Primary 17A30
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0311728-X
  • MathSciNet review: 0311728