On the Wedderburn principal theorem for nearly (1,1) algebras

Miles, T. J.

doi:10.1090/S0002-9947-1971-0306278-3

On the Wedderburn principal theorem for nearly $(1, 1)$ algebras
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by T. J. Miles PDF

Trans. Amer. Math. Soc. 161 (1971), 101-110 Request permission

Abstract:

A nearly $(1,1)$ algebra is a finite dimensional strictly power-associative algebra satisfying the identity $(x,x,y) = (x,y,x)$ where the associator $(x,y,z) = (xy)z - x(yz)$. An algebra A has a Wedderburn decomposition in case A has a subalgebra $S \cong A - N$ with $A = S + N$ (vector space direct sum) where N denotes the radical (maximal nil ideal) of A. D. J. Rodabaugh has shown that certain classes of nearly $(1,1)$ algebras have Wedderburn decompositions. The object of this paper is to expand these classes. The main result is that a nearly $(1,1)$ algebra A containing 1 over a splitting field of characteristic not 2 or 3 such that A has no nodal subalgebras has a Wedderburn decomposition.

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