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Fields

In: The Concise Handbook of Algebra

Author

Listed:
  • Shreeram S. Abhyankar

    (Lafayette)

  • Harald Niederreiter
  • Joseph J. Rotman
  • Andy R. Magid
  • A. V. Mikhalev
  • E. V. Pankratiev
  • T. Y. Lam
  • Franz Binder
  • Rudi Lidl

Abstract

After the initial impetus given to it by Dedekind and Weber (1882), the theory of field extensions was first systemized by Steinitz (1910). Chevalley (1951) is, in effect, an updated version of the Dedekind-Weber paper. Ultimately, traveling through the edifice of algebraic geometry, it acquired the form presented in Zariski and Samuel (1975). Indeed, it is not easy to decipher where the theory of field extensions ends and algebraic geometry begins. Its ubiquitous use in algebraic geometry can be seen in Abhyankar’s resolution of singularities book (Abhyankar 1998) and in the more heuristic introduction to it in his engineering book (Abhyankar 1990). The intimate relationship of field extensions to group theory is expounded in his recent survey article (Abhyankar 2001).

Suggested Citation

  • Shreeram S. Abhyankar & Harald Niederreiter & Joseph J. Rotman & Andy R. Magid & A. V. Mikhalev & E. V. Pankratiev & T. Y. Lam & Franz Binder & Rudi Lidl, 2002. "Fields," Springer Books, in: The Concise Handbook of Algebra, chapter 0, pages 355-381, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-3267-3_4
    DOI: 10.1007/978-94-017-3267-3_4
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