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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Derivation alternator rings with idempotent
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by Irvin R. Hentzel and Harry F. Smith
Trans. Amer. Math. Soc. 258 (1980), 245-256
DOI: https://doi.org/10.1090/S0002-9947-1980-0554331-7

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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Bibliographic 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