Geodesic
Commutative Non-Associative Algebras and Identities of Degree Four
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 769-794

Voir la notice de l'article provenant de la source Cambridge University Press

The main result of this paper is the following.Theorem 1. Let A be a simple, commutative, finite-dimensional algebra containing an idempotent over a field of characteristic 0, and let the algebra A' obtained from A by adjoining a unity element satisfy an identity of degree ≦ 4 not implied by commutativity. Then either A is a Jordan algebra or A is two-dimensional over an appropriate field E. 
Osborn, J. Marshall. Commutative Non-Associative Algebras and Identities of Degree Four. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 769-794. doi: 10.4153/CJM-1968-077-4
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[1] 1. Osborn, J. M., Identities on non-associative algebras, Can. J. Math. 17 (1965), 78–92. Google Scholar

[2] 2. Osborn, J. M., Commutative algebras satisfying an identity of degree four, Proc. Amer. Math. Soc. 16 (1965), 1114–1120. Google Scholar

[3] 3. Petersson, Holger, Ûber eine Verallgemeinerung von Jordan-Algebren, Dissertation, Univ. of Munich, 1965. Google Scholar

[4] 4. Schafer, R. D., An introduction to non-associative algebras (Academic Press, New York, 1966). Google Scholar

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