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Journal of Mathematical Sciences

, Volume 237, Issue 2, pp 254–262 | Cite as

Rolling Simplexes and Their Commensurability IV. A Farewell to Arms!*

  • O. V. GerasimovaEmail author
  • Yu. P. Razmyslov
Article
  • 8 Downloads

Abstract

This text by pure algebraic reasons outlines why the spectrum of maximal ideals SpecA 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 ψM : A → (M ∈ SpecA) and any a ∈ A the Taylor series \( {\overset{\sim }{\psi}}_M(a)\overset{\mathrm{def}}{=}\sum \limits_{m=0}^{\infty }{\psi}_M\left({a}^{(m)}\right)\frac{z^m}{m!} \) has nonzero radius of convergence depending on the element a ∈ A.

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Notes

References

  1. 1.
    O. V. Gerasimova, G. A. Pogudin, and Yu. P. Razmyslov, “Rolling simplexes and their commensurability, III (Capelli identities and their application to differential algebras),” Fundam. Prikl. Mat., 19, No. 6, 7–24 (2014).zbMATHGoogle Scholar
  2. 2.
    I. R. Shavarevich, Basic Algebraic Geometry, Springer, Berlin (1994).CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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