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Non-Associative Algebra and Its Applications pp 219–222Cite as

A Generalization of Novikov Rings

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 303))

Abstract

Generalizations of theorems on simple Novikov algebras by E. I. Zel’manov and J. M. Osborn to a subvariety in the join of associative and Novikov are obtained.

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References

  1. A. A. Balinskii and S. P. Novikov, Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras, Dokl. Akad. Nauk SSSR 283 (1985), 1036–1039; English Transi. Soviet Math. Dokl. 32 (1985), 228–231.

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  2. I. M. Gelfand and I. Ya. Dorfman, Hamiltonian operators and related algebraic structures, Funktsional Anal. I. Prolozhen, 13 No. 4 (1979), 13–30; English Transi. Funct. Anal. and Appl. 13 (1979), 248–262.

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  3. E. Kleinfeld, On rings satisfying (x, y, z) = (y, x, z), Algebras Groups Geom., 4 (1987), 129–138.

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  4. J. M. Osborn, Novikov algebras, Nova J. Algebra Geom., 1 (1992), 1–14.

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  5. J. M. Osborn, Simple Novikov algebras with an idempotent, Comm. Algebra, 20 No. 9 (1992), 2729–2753.

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  6. J. M. Osborn and E. I. Zelmanov, Nonassociative algebras related to Hamiltonian operators in the formal calculus of variations, to appear.

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  7. E. I. Zelmanov, On a class of local translation invariant Lie algebras, Soviet Math. Dokl. 35 (1987), 216–218; English Transi. Soviet Math. Dokl. 35 (1987), 216–218.

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, The University of Iowa, Iowa City, Iowa, 52242, USA

    Erwin Kleinfeld

  2. Department of Mathematics Statistics and Computing Science, University of New England, Armidale, N.S.W., 2351, Australia

    Harry F. Smith

Authors
  1. Erwin Kleinfeld
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  2. Harry F. Smith
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oviedo, Oviedo, Spain

    Santos González

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© 1994 Springer Science+Business Media Dordrecht

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Kleinfeld, E., Smith, H.F. (1994). A Generalization of Novikov Rings. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_36

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  • DOI: https://doi.org/10.1007/978-94-011-0990-1_36

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4429-5

  • Online ISBN: 978-94-011-0990-1

  • eBook Packages: Springer Book Archive

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