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Proceedings of the American Mathematical Society

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Irreducible polynomial identities in anticommutative algebras


Authors: Seymour Kass and William G. Witthoft
Journal: Proc. Amer. Math. Soc. 26 (1970), 1-9
MSC: Primary 17.60
MathSciNet review: 0260818
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Abstract: The methods introduced by J. M. Osborn for isolating those polynomial identities worth studying in commutative algebras are here modified to yield three theorems for anticommutative algebras. The first establishes a practical criterion for the irreducibility of polynomial identities; the others list all canonical polynomials of low degree that are irreducible relative to anticommutativity.


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

  • [1] Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0143793
  • [2] J. Marshall Osborn, Identities of non-associative algebras, Canad. J. Math. 17 (1965), 78–92. MR 0179221
  • [3] Arthur A. Sagle, On simple extended Lie algebras over fields of characteristic zero, Pacific J. Math. 15 (1965), 621–648. MR 0190198

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0260818-6
Keywords: Nonassociative algebras, anticommutative algebras, irreducible polynomial identities, free nonassociative algebra, linearization
Article copyright: © Copyright 1970 American Mathematical Society