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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 Appl. Math., no. 10, Interscience, New York, 1962. MR 26 #1345. MR 0143793 (26:1345)
  • [2] J. Marshall Osborn, Identities of non-associative algebras, Canad. J. Math. 17 (1965), 78-92. MR 31 #3470. MR 0179221 (31:3470)
  • [3] A. A. Sagle, On simple extended Lie algebras over fields of characteristic zero, Pacific J. Math. 15 (1965), 621-648. MR 32 #7612. MR 0190198 (32:7612)

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Keywords: Nonassociative algebras, anticommutative algebras, irreducible polynomial identities, free nonassociative algebra, linearization
Article copyright: © Copyright 1970 American Mathematical Society

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