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On a class of power-associative periodic rings

Published online by Cambridge University Press:  17 April 2009

J.A. Loustau
J.A. Loustau
Affiliation:
University of California at Santa Barbara, Santa Barbara, California, USA.
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Abstract

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A power-associative ring A is called a p-ring provided there exists a prime p so that for every x in A, xp = x and px = 0. It is shown that if A is such a ring with p ≠ 2, then A is isomorphic to a subdirect sum of copies of GF(p), the Galois field with p elements.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 357 - 362
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Goldman, Jerry and Kass, Seymour, “Linearization in rings and algebras”, Amer. Math. Monthly. 76 (1969), 348–355.CrossRefGoogle Scholar
[2]Jacobson, Nathan, Structure and representations of Jordan algebras (Colloquium Publ. 39. Amer. Math. Soc., Providence, Rhode Island, 1968).CrossRefGoogle Scholar
[3]McCoy, Neal H., Rings and ideals (Carus Mathematical Monographs, No. 8. Mathematical Association of America; John Wiley & Sons, New York, 1948).CrossRefGoogle Scholar
[4]McCrimmon, Kevin, “Finite power-associative division rings”, Proc. Amer. Math. Soc. 17 (1966), 1173–1177.CrossRefGoogle Scholar
[5]Schafer, Richard D., An introduction to nonassociative algebras (Academic Press, New York, London, 1966).Google Scholar