Geodesic
A Generalization of Commutative and Alternative Rings
Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 348-362

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

In [3] Schafer has defined generalized standard rings as rings satisfying the identities (1) (2) (3) and observed that these identities imply (y,y, (x, z)) = 0 and if the characteristic is not three, (x, y, x 2) = 0. Schafer determined the structure of simple, finite-dimensional generalized standard algebras of characteristic not two or three by showing that they must be either commutative, Jordan, or alternative.Previously one of us [2] had studied accessible rings, which are defined by the identities (x,y,z) + (z,x,y) – (x,z,y) = 0 and ((w,x), y,z) = 0. 
Kleinfeld, Erwin; Kleinfeld, Margaret Humm; Kosier, Frank. A Generalization of Commutative and Alternative Rings. Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 348-362. doi: 10.4153/CJM-1970-043-7
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[1] 1. Albert, A. A., Power associative rings, Trans. Amer. Math. Soc. 64 (1948), 552–593. Google Scholar

[2] 2. Erwin, Kleinfeld, Standard and accessible rings, Can. J. Math. 8 (1956), 335–340. Google Scholar

[3] 3. Schafer, R. D., On generalized standard algebras, Proc. Nat. Acad. Sci. U.S.A. 60 (1968) 73–74. Google Scholar

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