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Rings Satisfying (x, y, z) = (y, z, x)
Published online by Cambridge University Press: 20 November 2018
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Let R be a ring satisfying the identity
1
for all x, y, z ϵ R, where (x,y,z) = (xy)z — x(yz). If R also satisfies the identity (x, x, x) = 0 for all x ϵ R, then R is alternative. It is known that if R satisfies (1), it need not be an alternative (see 6). Thus, the class of rings satisfying (1) is a non-trivial extension of the class of alternative rings. P. Jordan remarked that (x, x, x)2 = 0 is an identity in R (see 9).
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- Copyright © Canadian Mathematical Society 1968
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