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  3. Arithmetic of Blowup Algebras
  • Cited by 115
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2009
      February 1994
      ISBN:
      9780511574726
      9780521454841
      DOI:
      https://doi.org/10.1017/CBO9780511574726
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.483kg, 340 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      London Mathematical Society Lecture Note Series (195)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    London Mathematical Society Lecture Note Series (195)
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    Book description

    This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.

    Reviews

    ‘…an interesting collection of facts not easily found elsewhere.’

    Source: Mathematika

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