Derivation alternator rings with idempotent
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- by Irvin R. Hentzel and Harry F. Smith PDF
- Trans. Amer. Math. Soc. 258 (1980), 245-256 Request permission
Abstract:
A nonassociative ring is called a derivation alternator ring if it satisfies the identities $(yz, x, x) = y(z, x, x) + (y, x, x)z, (x, x, yz) = y(x, x, z) + (x, x, y)z$ and $(x, x, x) = 0$. Let R be a prime derivation alternator ring with idempotent $e \ne 1$ and characteristic $\ne 2$. If R is without nonzero nil ideals of index 2, then R is alternative.References
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- Erwin Kleinfeld, Generalization of alternative rings. I, II, J. Algebra 18 (1971), 304-325; ibid. 18 (1971), 326–339. MR 0274545, DOI 10.1016/0021-8693(71)90063-9
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 258 (1980), 245-256
- MSC: Primary 17A30; Secondary 17D05
- DOI: https://doi.org/10.1090/S0002-9947-1980-0554331-7
- MathSciNet review: 554331