Scalar dependent algebras
Authors: Raymond Coughlin, Erwin Kleinfeld and Michael Rich
Journal: Proc. Amer. Math. Soc. 39 (1973), 69-72
MSC: Primary 17A30
MathSciNet review: 0311728
Abstract: An algebra over a field will be called scalar dependent in case for every in there exists a function in such that . 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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