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Fundam. Prikl. Mat., 2008, Volume 14, Issue 4, Pages 121–135 (Mi fpm1129)  

This article is cited in 2 scientific papers (total in 2 papers)

One-element differential standard bases with respect to inverse lexicographical orderings

A. I. Zobnin

M. V. Lomonosov Moscow State University

Abstract: We give a simplified proof of the following fact: for all nonnegative integers $n$ and $d$ the monomial $y_n^d$ forms a differential standard basis of the ideal $[y_n^d]$. In contrast to Levi's combinatorial proof, in this proof we use the Gröbner bases technique. Under some assumptions we prove the converse result: if an isobaric polynomial $f$ forms a differential standard basis of $[f]$, then $f=y_n^d$.

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English version:
Journal of Mathematical Sciences (New York), 2009, 163:5, 523–533

Bibliographic databases:

UDC: 512.628.2

Citation: A. I. Zobnin, “One-element differential standard bases with respect to inverse lexicographical orderings”, Fundam. Prikl. Mat., 14:4 (2008), 121–135; J. Math. Sci., 163:5 (2009), 523–533

Citation in format AMSBIB
\Bibitem{Zob08}
\by A.~I.~Zobnin
\paper One-element differential standard bases with respect to inverse lexicographical orderings
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 4
\pages 121--135
\mathnet{http://mi.mathnet.ru/fpm1129}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2482037}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 163
\issue 5
\pages 523--533
\crossref{https://doi.org/10.1007/s10958-009-9690-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70649098155}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. V. Gerasimova, Yu. P. Razmyslov, G. A. Pogudin, “Rolling simplexes and their commensurability. III (Capelli identities and their application to differential algebras)”, J. Math. Sci., 221:3 (2017), 315–325  mathnet  crossref  mathscinet
    2. G. A. Pogudin, “Primary differential nil-algebras do exist”, Moscow University Mathematics Bulletin, 69:1 (2014), 33–36  mathnet  crossref  mathscinet
  • Фундаментальная и прикладная математика
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