Geodesic
A Generalization of Degree Two Simple Finite-Dimensional Noncommutative Jordan Algebras
Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 480-493

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Let be an algebra over a field . For x, y, z in , write (x, y, z) = (xy)z – x(yz) and x-y = xy + yx. The attached algebra is the same vector space as , but the product of x and y is x · y. We aim to prove the following result.THEOREM 1. Let be a finite-dimensional, power-associative, simple algebra of degree two over a field of prime characteristic greater than five. For all x, y, z in , suppose 1 Then is noncommutative Jordan.The proof of Theorem 1 falls into three main sections. In § 3 we establish some multiplication properties for elements of the subspace in the Peirce decomposition . In §4 we construct an ideal of which we then use to show that the nilpotent elements of form a subalgebra of for i = 0, 1. 
Conlon, Mary Ellen. A Generalization of Degree Two Simple Finite-Dimensional Noncommutative Jordan Algebras. Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 480-493. doi: 10.4153/CJM-1980-038-1
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[1] 1. Albert, A. A., A theory of power-associative commutative algebras, Trans. Amer. Math. Soc. 69 (1950), 503–527. Google Scholar

[2] 2. Anderson, C. T., On an identity common to Lie, Jordan, and quasias so dative algebras, Ph.D. thesis, Ohio State University (1964). Google Scholar

[3] 3. Florey, F. G., A generalization of noncommutative Jordan algebras, J. Algebr. 23 (1972), 502–518. Google Scholar

[4] 4. Goldman, J. I. and Kokoris, L. A., Generalized simple noncommutative Jordan algebras of degree two, J. Algebr. 42 (1976), 472–482. Google Scholar

[5] 5. Kosier, F., A generalization of alternative rings, Trans. Amer. Math. Soc. 112 (1964), 32–42. Google Scholar

[6] 6. Morgan, R. V. Jr., On a generalization of alternative rings, Can. J. Math. 22 (1970), 953–966. Google Scholar

[7] 7. Schafer, R. D., An introduction to nonassociative algebras (Academic Press, New York, 1966). Google Scholar

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