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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Absolute zero divisors and local nilpotence in alternative algebras

Author: Kevin McCrimmon
Journal: Proc. Amer. Math. Soc. 47 (1975), 293-299
MathSciNet review: 0354795
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Abstract | References | Additional Information

Abstract: It has been conjectured that absolute zero divisors generate locally nilpotent ideals in Jordan and alternative algebras. A. M. Slin'ko has recently established this result for special Jordan algebras; in this note we show how his method can be modified to establish the result for alternative algebras.

References [Enhancements On Off] (What's this?)

  • [1] K. McCrimmon, Alternative algebras satisfying polynomial identities, J. Algebra 24 (1973), 283-292. MR 0311736 (47:298)
  • [2] A. M. Slin'ko, On the Jacobson radical and absolute zero divisors in special Jordan algebras, Algebra i Logika 11 (1972), 711-723. (Russian) MR 0316518 (47:5065)
  • [3] E. Kleinfeld, Alternative nil rings, Ann. of Math. (2) 66 (1957), 395-399. MR 19, 383. MR 0087638 (19:383a)

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Keywords: Absolute zero divisor, locally nilpotent, alternative algebra
Article copyright: © Copyright 1975 American Mathematical Society

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