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An Improved Version of Standard Bases

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Formal Power Series and Algebraic Combinatorics

Abstract

Our main goal is rather methodical, namely, to give an improved general version of standard bases. For same recent attempts in this direction, see author’s articles [1], [2]. In such a way we make examples more accurate and extend the area of applications. We begin with the basic definitions in order the paper to be self-contained.

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References

  1. Latyshev, V. N.: Canonization and Standard Bases of Filtered Structures. Transactions of the Second International Taiwan-Moscow Algebra Workshop, Berlin, New-York, 1997 (to appear)

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  2. Latyshev, V. N.: General Version of Standard Bases in Linear Structures, Algebra. Proceedings of the Int. Alg. Conf. on the Occasion of the 90th Birthday of A. G. Kurosh, Moscow, Russia, May 25–30, 1998, Berlin, 2000 (to appear)

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  3. Newman, M. H.: On Theories with a Combinatorial Definition of “Equivalence”. Aim. Math. 43:2 (1942) 223–243

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  4. Gerdt, V. P., Blinkov, Y. A.: Involutive Bases of Polynomial Ideals. Preprint. Joint Inst. for Nuclear Research, Dubna, Russia, (1996) 1–25

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  5. Shirshov, A. I.: Some Algorithmic Problems on Lie Algebras. Sibirskii Math. Zhurnal. 3 (1962) 292–296 (in Russian)

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  6. Mikhalev, A. A.: The Composition Lemma for Color Lie Superalgebras and for Lie P-Algebras. Contemporary Math. 131 (1992)

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Author information

Authors and Affiliations

  1. Moscow State University, Russia

    V. N. Latyshev

Authors
  1. V. N. Latyshev
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Editor information

Editors and Affiliations

  1. LIAFA, Université Paris VII, 2, Place Jussieu, 75251, Paris Cedex 05, France

    Daniel Krob

  2. Moscow State University, 119899, Moscow, Russia

    Alexander A. Mikhalev  & Alexander V. Mikhalev  & 

  3. The University of Hong Kong, Hong Kong

    Alexander A. Mikhalev

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© 2000 Springer-Verlag Berlin Heidelberg

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Latyshev, V.N. (2000). An Improved Version of Standard Bases. In: Krob, D., Mikhalev, A.A., Mikhalev, A.V. (eds) Formal Power Series and Algebraic Combinatorics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04166-6_47

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  • DOI: https://doi.org/10.1007/978-3-662-04166-6_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08662-5

  • Online ISBN: 978-3-662-04166-6

  • eBook Packages: Springer Book Archive

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