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On a Generalization of Alternative Rings

Published online by Cambridge University Press:  20 November 2018

Raymond V. Morgan Jr.
Raymond V. Morgan Jr.*
Affiliation:
Southern Methodist University, Dallas, Texas
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Bruck and Kleinfeld [3] proved that any alternative ring with characteristic prime to 2 must satisfy the identity

where the associator (x,y,z) is defined by (x, y, z) = (xy)z – x(yz) and . Linearization of the identity (x2, y, z) = 2x · (x, y, z) yields for characteristic prime to 2 an equivalent identity

(1)

Using the right alternative law (x, y, z) = –(y, x, z) and the flexible law (x, y, z) = –(z, y, x) which is satisfied in any alternative ring we obtain

(2)

and

(3)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 953 - 966
Copyright
Copyright © Canadian Mathematical Society 1970

References

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