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.References
- Raymond Coughlin and Michael Rich, On scalar dependent algebras, Canadian J. Math. 24 (1972), 696–702. MR 296116, DOI 10.4153/CJM-1972-065-5
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