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Spec (R)

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1358)

Abstract

It is possible to associate a “geometric” object to an arbitrary commutative ring R. This object will be called Spec (R). If R is a finitely generated integral domain over an algebraically closed field, Spec (R) will be very nearly the same as an affine variety associated to R in Chapter I. However in this section we will be completely indifferent to any special properties that R may or may not have — e.g., whether R has nilpotents or other zero-divisors in it or not; whether or not R has a large subfield over which it is finitely generated or even any subfield at all. We insist only that R be commutative and have a unit element 1.

Keywords

  • Prime Ideal
  • Maximal Ideal
  • Closed Point
  • Valuation Ring
  • Irreducible Polynomial

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1988 Springer-Verlag Berlin Heidelberg

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Mumford, D. (1988). Spec (R). In: The Red Book of Varieties and Schemes. Lecture Notes in Mathematics, vol 1358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21581-4_11

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  • DOI: https://doi.org/10.1007/978-3-662-21581-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50497-9

  • Online ISBN: 978-3-662-21581-4

  • eBook Packages: Springer Book Archive