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Directed Unions of Local Quadratic Transforms of Regular Local Rings and Pullbacks

In: Rings, Polynomials, and Modules

Author

Listed:
  • Lorenzo Guerrieri

    (UniversitΓ  di catania)

  • William Heinzer

    (Purdue University, Department of Mathematics)

  • Bruce Olberding

    (New Mexico State University, Department of Mathematical Sciences)

  • Matthew Toeniskoetter

    (Purdue University, Department of Mathematics)

Abstract

Let { R n , π”ͺ n } n β‰₯ 0 $$\{R_{n},\mathfrak{m}_{n}\}_{n\geq 0}$$ be an infinite sequence of regular local rings with R n+1 birationally dominating R n and π”ͺ n R n + 1 $$\mathfrak{m}_{n}R_{n+1}$$ a principal ideal of R n+1 for each n. We examine properties of the integrally closed local domain S = ⋃ n β‰₯ 0 R n $$S =\bigcup _{n\geq 0}R_{n}$$ .

Suggested Citation

  • Lorenzo Guerrieri & William Heinzer & Bruce Olberding & Matthew Toeniskoetter, 2017. "Directed Unions of Local Quadratic Transforms of Regular Local Rings and Pullbacks," Springer Books, in: Marco Fontana & Sophie Frisch & Sarah Glaz & Francesca Tartarone & Paolo Zanardo (ed.), Rings, Polynomials, and Modules, pages 257-280, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-65874-2_13
    DOI: 10.1007/978-3-319-65874-2_13
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