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On Cayley-Dickson Rings

Published online by Cambridge University Press:  20 November 2018

Daniel J. Britten
Daniel J. Britten*
Affiliation:
University of Windsor, Windsor, Ontario
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M. Slater has shown that a prime alternative (not associative) ring R such that 3R≠0 is a Cayley-Dickson ring, [7], That is, if F is the field of quotients of the center, Z, of R then F ⊗Z R is a Cayley-Dickson algebra.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975, pp. 625 - 627
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Albert, A. A., On simple alternative rings, Canad. J. Math. 4 (1952), 129–135.Google Scholar
2. Britten, D. J., Goldie-like conditions on Jordan matrix rings, Ph.D. thesis, The Univ. of Iowa (1971).Google Scholar
3. Jacobson, N., Structure and Representations of Jordan Algebras, American Mathematical Society, (1968).Google Scholar
4. Kleinfeld, E., Primitive alternative rings and semi-simplicity, Amer. J. Math. 77 (1955), 725–730.Google Scholar
5. Kleinfeld, E., Alternative nil rings, Ann. Amer. Math. Soc. 66 (1957), 395–399.Google Scholar
6. Martindale, W. S., Rings with involution and polynomial identities, J. Algebra, 2 (1969), 186–194.Google Scholar
7. Slater, M., Prime alternative rings, I, J. Algebra, 15 (1970), 229–243.Google Scholar