The Algebraic View of Infinitesimal Notions

  • Igor R. Shafarevich
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 11)


Considering quantities ‘up to infinitesimals of order n’ can be translated in algebraic terms quite conveniently, considering elements ε (of certain rings) satisfying ε n = 0 as analogues of infinitesimals. Suppose, for example, that C is an algebraic curve, for simplicity considered over the complex field ℂ.


Singular Point Tangent Space Maximal Ideal Formal Power Series Number Field 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Igor R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of ScienceMoscowRussia

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