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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0260818-6
MathSciNet review:
0260818
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Abstract | References | Similar Articles | Additional Information
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.
- 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
- J. Marshall Osborn, Identities of non-associative algebras, Canadian J. Math. 17 (1965), 78–92. MR 179221, DOI https://doi.org/10.4153/CJM-1965-008-3
- Arthur A. Sagle, On simple extended Lie algebras over fields of characteristic zero, Pacific J. Math. 15 (1965), 621–648. MR 190198
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Additional Information
Keywords:
Nonassociative algebras,
anticommutative algebras,
irreducible polynomial identities,
free nonassociative algebra,
linearization
Article copyright:
© Copyright 1970
American Mathematical Society