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On a Wedderburn principal theorem for the flexible algebras


Author: Robert A. Chaffer
Journal: Trans. Amer. Math. Soc. 193 (1974), 217-229
MSC: Primary 17A20
DOI: https://doi.org/10.1090/S0002-9947-1974-0349775-X
MathSciNet review: 0349775
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Abstract: A strictly power-associative algebra A over a field K is said to have a Wedderburn decomposition if there is a subalgebra S of A such that $ A = S + N$, where N is the nil radical of A, and $ S = A - N$. A Wedderburn principal theorem for a class of algebras is a theorem which asserts that the algebras A, in the class, with $ A - N$ separable have Wedderburn decompositions. It is known that there is no such theorem for the class of noncommutative Jordan algebras. A partial result in this direction is the following theorem.

Theorem. Let A be a strictly power-associative, flexible algebra over a field F with characteristic not 2 or 3, with $ A - N$ separable and such that $ A = {A_1} \oplus {A_2} \oplus \cdots \oplus {A_n}$ where each $ {A_i}$. has $ {A_i} - {N_i}$ simple and has more than two pairwise orthogonal idempotents. Then $ A = S + N$ where S is a subalgebra of A.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0349775-X
Keywords: Wedderburn decomposition, flexible algebras, noncommutative Jordan algebra, quasiassociative algebra, power-associative algebra
Article copyright: © Copyright 1974 American Mathematical Society

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