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Moscow University Mathematics Bulletin

, Volume 72, Issue 3, pp 89–93 | Cite as

Nonaffine differential-algebraic curves do not exist

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Abstract

The paper outlines why the spectrum of maximal ideals Spec A of a countable-dimensional differential ℂ-algebra A of transcendence degree 1 without zero divisors is locally analytic, which means that for any ℂ-homomorphism ψ M: A → ℂ (MSpec A) and any aA the Taylor series \(\widetilde {{\psi _M}}{\left( a \right)^{\underline{\underline {def}} }}\sum\limits_{m = 0}^\infty {\psi M\left( {{a^{\left( m \right)}}} \right)} \frac{{{z^m}}}{{m!}}\) has nonzero radius of convergence depending on the element aA.

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References

  1. 1.
    I. R. Shafarevich, Foundation of Algebraic Geometry (MCCME, Moscow, 2007) [in Russian].Google Scholar
  2. 2.
    O. V. Gerasimova, G. A. Pogudin, and Yu. P. Razmyslov, “Rolling Simplexes and Their Commensurability, III (Capelli Relations and Their Applications in Differential Algebras),” Fund. Prikl. Matem. 19 (6), 7 (2014).Google Scholar

Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Moscow State UniversityFaculty of Mechanics and Mathematics, Leninskie GoryMoscowRussia

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