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  • © 2014

Commutative Algebra

Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions

Editors:

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  • Contributions cover the flourishing areas of commutative algebra, not yet well represented in published literature

  • Contains 100 open problems supplied by the authors

  • Provides a multi-dimensional survey of the recent development of the field and an extensive bibliography

  • Includes supplementary material: sn.pub/extras

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USD 99.00
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  • ISBN: 978-1-4939-0925-4
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Softcover Book
USD 129.00
Price excludes VAT (USA)
Hardcover Book
USD 139.99
Price excludes VAT (USA)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-viii
  2. Weak Global Dimension of Prüfer-Like Rings

    • Khalid Adarbeh, Salah-Eddine Kabbaj
    Pages 1-23
  3. Quasi-complete Semilocal Rings and Modules

    • Daniel D. Anderson
    Pages 25-37
  4. Prime Ideals in Polynomial and Power Series Rings over Noetherian Domains

    • Ela Celikbas, Christina Eubanks-Turner, Sylvia Wiegand
    Pages 55-82
  5. On Boolean Subrings of Rings

    • Ivan Chajda, Günther Eigenthaler
    Pages 113-117
  6. On a New Class of Integral Domains with the Portable Property

    • David E. Dobbs, Gabriel Picavet, Martine Picavet-L’Hermitte
    Pages 119-132
  7. The Probability That Int n (D) Is Free

    • Jesse Elliott
    Pages 133-151
  8. Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey

    • Carmelo Antonio Finocchiaro, Marco Fontana, K. Alan Loper
    Pages 153-173
  9. Ten Problems on Stability of Domains

    • Stefania Gabelli
    Pages 175-193
  10. How to Construct Huge Chains of Prime Ideals in Power Series Rings

    • Byung Gyun Kang, Phan Thanh Toan
    Pages 225-238
  11. Prime Ideals That Satisfy Hensel’s Lemma

    • Stephen McAdam
    Pages 255-268
  12. Finitely Stable Rings

    • Bruce Olberding
    Pages 269-291
  13. Integral Closure of Rings of Integer-Valued Polynomials on Algebras

    • Giulio Peruginelli, Nicholas J. Werner
    Pages 293-305
  14. Integral Closure

    • Irena Swanson
    Pages 331-351

About this book

This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions.

Specific topics include:

·    Homological dimensions of Prüfer-like rings

·    Quasi complete rings

·    Total graphs of rings

·    Properties of prime ideals over various rings

·    Bases for integer-valued polynomials

·    Boolean subrings

·    The portable property of domains

·    Probabilistic topics in Intn(D)

·    Closure operations in Zariski-Riemann spaces of valuation domains

·    Stability of domains

·    Non-Noetherian grade

·    Homotopy in integer-valued polynomials

·    Localizations of global properties of rings

·    Topics in integral closure

·    Monoids and submonoids of domains

The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.

Keywords

  • Graz conference proceedings
  • Kronecker function rings
  • Lerenzen Monoids
  • commutative algebra
  • integer-valued polynomials
  • polynomial functions
  • power series rings

Editors and Affiliations

  • Dipartimento di Matematica, Università degli Studi Roma Tre, Rome, Italy

    Marco Fontana

  • Department of Mathematics, Graz University of Technology, Graz, Austria

    Sophie Frisch

  • Department of Mathematics, University of Connecticut, Storrs, USA

    Sarah Glaz

Bibliographic Information

Buying options

eBook
USD 99.00
Price excludes VAT (USA)
  • ISBN: 978-1-4939-0925-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 129.00
Price excludes VAT (USA)
Hardcover Book
USD 139.99
Price excludes VAT (USA)