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Standard and Accessible Rings

Published online by Cambridge University Press:  20 November 2018

Erwin Kleinfeld
Erwin Kleinfeld*
Affiliation:
Ohio State University
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1. Introduction. A ring is defined to be standard (1) in case the following two identities hold :

(1) (wx, y, z) + (xz, y, w) + (wz, y, x) = 0,

(2) (x, y, z) + (z, x, y) − (x, z, y) = 0,

where the associator (x, y, z) is defined by (x, y, z) = (xy)z − x(yz). Albert has determined the structure of finite-dimensional, standard algebras (1).

The simple ones turn out to be either Jordan algebras or associative ones.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 335 - 340
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Albert, A. A., Power-associative rings, Trans. Amer. Math. Soc, 64 (1948), 552–593.Google Scholar
2. Brown, Bailey, An extension of the Jacobson radical, Proc. Amer. Math. Soc, 2 (1951), 114–117.Google Scholar