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An Extension of the Class of Alternative Rings
Published online by Cambridge University Press: 20 November 2018
Extract
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
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- Copyright © Canadian Mathematical Society 1965
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