Absolute zero divisors and local nilpotence in alternative algebras
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- by Kevin McCrimmon PDF
- Proc. Amer. Math. Soc. 47 (1975), 293-299 Request permission
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
- Kevin McCrimmon, Alternative algebras satisfying polynomial identities, J. Algebra 24 (1973), 283–292. MR 311736, DOI 10.1016/0021-8693(73)90138-5
- A. M. Slin′ko, The Jacobson radical and absolute divisors of zero of special Jordan algebras, Algebra i Logika 11 (1972), 711–723, 737 (Russian). MR 0316518
- Erwin Kleinfeld, Alternative nil rings, Ann. of Math. (2) 66 (1957), 395–399. MR 87638, DOI 10.2307/1969897
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 293-299
- DOI: https://doi.org/10.1090/S0002-9939-1975-0354795-1
- MathSciNet review: 0354795