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An Extension of the Class of Alternative Rings

Published online by Cambridge University Press:  20 November 2018

D. L. Outcalt
D. L. Outcalt*
Affiliation:
Claremont Men's College, Claremont, California
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Define R to be a ring of characteristic not 2 or 3 satisfying the identity

(1)       (x,y,z) = (y,z,x)

for all x, y, z ∊ R, where by characteristic not p is meant x —> px is a one-toone mapping of R upon R. The associator (a, b, c) of R is defined by (a, b, c) = ab·c — a·bc. lf R also satisfies the identity

(2)      (x, x, x) = 0

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 130 - 141
Copyright
Copyright © Canadian Mathematical Society 1965

References

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