Rings, Polynomials, and Modules

  • Marco Fontana
  • Sophie Frisch
  • Sarah Glaz
  • Francesca Tartarone
  • Paolo Zanardo

Table of contents

  1. Front Matter
    Pages i-viii
  2. Daniel D. Anderson, Erik Hasse
    Pages 1-11
  3. Gerhard Angermüller
    Pages 13-31
  4. Jacques Boulanger, Jean-Luc Chabert
    Pages 79-101
  5. Ilaria Castellano, Anna Giordano Bruno
    Pages 103-127
  6. Alfred Geroldinger, Wolfgang A. Schmid, Qinghai Zhong
    Pages 191-235
  7. Lorenzo Guerrieri, William Heinzer, Bruce Olberding, Matthew Toeniskoetter
    Pages 257-280
  8. Thomas G. Lucas
    Pages 281-298
  9. Gabriel Picavet, Martine Picavet-L’Hermitte
    Pages 307-336
  10. Roswitha Rissner
    Pages 337-352

About this book

Introduction

This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. 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, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra.

Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: “Recent Advances in Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and Polynomials”  Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.

Keywords

Gaussian properties of rings Prufer domains Zariski-Riemann spaces divisibility properties commutative rings factorization theory in rings and semigroups fully inert modules homological algebra integer-valued polynomials linear algebra over rings module theory multiplicative ideal theory polynomial functions quasi-injective modules star operations topological entropy valuation rings

Editors and affiliations

  • Marco Fontana
    • 1
  • Sophie Frisch
    • 2
  • Sarah Glaz
    • 3
  • Francesca Tartarone
    • 4
  • Paolo Zanardo
    • 5
  1. 1.Dipartimento di Matematica e FisicaUniversità degli Studi Roma TreRomeItaly
  2. 2.Department of Analysis and Number TheoryGraz University of TechnologyGrazAustria
  3. 3.Department of MathematicsUniversity of ConnecticutStorrsUSA
  4. 4.Dipartimento di Matematica e FisicaUniversità degli Studi Roma TreRomeItaly
  5. 5.Dipartimento di MatematicaUniversità di PadovaPadovaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-65874-2
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-65872-8
  • Online ISBN 978-3-319-65874-2
  • About this book