Geodesic
A Generalization of Commutative and Alternative Rings II
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 728-733

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

We shall call a linear function on the elements of a ring R skew-symmetric if it vanishes whenever at least two of the variables are equal. Here we shall study rings R of characteristic not 2 which satisfy the following two identities: 1 (2) is skew-symmetric.Both of these identities hold in alternative rings. The fact that F(w, x, y, z) is skew-symmetric in alternative rings is an important tool in the study of such rings. It is also obvious that both identities hold in commutative rings. But unlike other recent generalizations of commutative and alternative rings it turns out that there exist simple, finite dimensional algebras of degree two which are neither alternative nor commutative and satisfy (1) and (2). 
Kleinfeld, Erwin. A Generalization of Commutative and Alternative Rings II. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 728-733. doi: 10.4153/CJM-1972-068-7
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[1] 1. Albert, A. A., On simple alternative rings, Can. J. Math. 4 (1952), 129–135. Google Scholar

[2] 2. Erwin, Kleinfeld, Quasi-nil rings, Proc. Amer. Math. Soc. 10 (1959), 477–479. Google Scholar

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