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


Consider some domain V in space and the vector fields defined on it. These can be added and multiplied by numbers, carrying out these operations on vectors applied to one point. Thus all vector fields form an infinite-dimensional vector space. But in addition to this, they can be multiplied by functions.


Vector Space Vector Field Tensor Product Integral Domain Polynomial Ring 
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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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