© 2014

Commutative Algebra

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

  • Marco Fontana
  • Sophie Frisch
  • Sarah Glaz
  • 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:


Table of contents

  1. Front Matter
    Pages i-viii
  2. Khalid Adarbeh, Salah-Eddine Kabbaj
    Pages 1-23
  3. Daniel D. Anderson
    Pages 25-37
  4. Ela Celikbas, Christina Eubanks-Turner, Sylvia Wiegand
    Pages 55-82
  5. Ivan Chajda, Günther Eigenthaler
    Pages 113-117
  6. David E. Dobbs, Gabriel Picavet, Martine Picavet-L’Hermitte
    Pages 119-132
  7. Jesse Elliott
    Pages 133-151
  8. Carmelo Antonio Finocchiaro, Marco Fontana, K. Alan Loper
    Pages 153-173
  9. Stefania Gabelli
    Pages 175-193
  10. Byung Gyun Kang, Phan Thanh Toan
    Pages 225-238
  11. Stephen McAdam
    Pages 255-268
  12. Bruce Olberding
    Pages 269-291
  13. Giulio Peruginelli, Nicholas J. Werner
    Pages 293-305
  14. 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.


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

Editors and affiliations

  • Marco Fontana
    • 1
  • Sophie Frisch
    • 2
  • Sarah Glaz
    • 3
  1. 1.Dipartimento di MatematicaUniversità degli Studi Roma TreRomeItaly
  2. 2.Department of MathematicsGraz University of TechnologyGrazAustria
  3. 3.Department of MathematicsUniversity of ConnecticutStorrsUSA

Bibliographic information

  • Book Title Commutative Algebra
  • Book Subtitle Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions
  • Editors Marco Fontana
    Sophie Frisch
    Sarah Glaz
  • DOI
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4939-0924-7
  • Softcover ISBN 978-1-4939-4741-6
  • eBook ISBN 978-1-4939-0925-4
  • Edition Number 1
  • Number of Pages VIII, 375
  • Number of Illustrations 20 b/w illustrations, 0 illustrations in colour
  • Topics Commutative Rings and Algebras
    Category Theory, Homological Algebra
    Algebraic Topology