Moscow University Mathematics Bulletin

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

Nonaffine differential-algebraic curves do not exist



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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    I. R. Shafarevich, Foundation of Algebraic Geometry (MCCME, Moscow, 2007) [in Russian].Google Scholar
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    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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