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Advances in Rings, Modules and Factorizations

Graz, Austria, February 19-23, 2018

  • Conference proceedings
  • © 2020

Overview

Editors:
  1. Alberto Facchini

    1. Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padua, Italy

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  2. Marco Fontana

    1. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Rome, Italy

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  3. Alfred Geroldinger

    1. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Graz, Austria

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  4. Bruce Olberding

    1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

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  • Represents a wide range of research trends in the area of commutative and noncommutative ring theory and their modules, with an emphasis on the interaction between quite different viewpoints and techniques
  • Shows that how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches
  • Is an excellent resource for scholars in the fields represented, as well as graduate students seeking an entryway into current research in algebra

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 321)

Included in the following conference series:

Conference proceedings info: Rings and Factorizations 2018.

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Table of contents (18 papers)

  1. Front Matter

    Pages i-viii
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  2. Commutative Rings Whose Principal Ideals Have Unique Generators

    • P. N. Ánh, Keith A. Kearnes, Ágnes Szendrei
    Pages 1-9

  3. On Monoids of Ideals of Orders in Quadratic Number Fields

    • Johannes Brantner, Alfred Geroldinger, Andreas Reinhart
    Pages 11-54

  4. UMT-domains: A Survey

    • Gyu Whan Chang
    Pages 55-77

  5. The Apéry Set of a Good Semigroup

    • Marco D’Anna, Lorenzo Guerrieri, Vincenzo Micale
    Pages 79-104

  6. On Syzygies for Rings of Invariants of Abelian Groups

    • M. Domokos
    Pages 105-124

  7. A Bazzoni-Type Theorem for Multiplicative Lattices

    • Tiberiu Dumitrescu
    Pages 125-133

  8. What is the Spectral Category?

    • María José Arroyo Paniagua, Alberto Facchini, Marino Gran, George Janelidze
    Pages 135-152

  9. A Survey on the Local Invertibility of Ideals in Commutative Rings

    • Carmelo Antonio Finocchiaro, Francesca Tartarone
    Pages 153-168

  10. Idempotence and Divisoriality in Prüfer-Like Domains

    • Marco Fontana, Evan Houston, Mi Hee Park
    Pages 169-182

  11. Simultaneous Interpolation and P-adic Approximation by Integer-Valued Polynomials

    • Sophie Frisch
    Pages 183-192

  12. Length Functions over Prüfer Domains

    • Gabriele Fusacchia, Luigi Salce
    Pages 193-216

  13. On Some Arithmetical Properties of Noetherian Domains

    • Florian Kainrath
    Pages 217-222

  14. Spectral Spaces Versus Distributive Lattices: A Dictionary

    • Henri Lombardi
    Pages 223-245

  15. Valuative Marot Rings

    • Thomas G. Lucas
    Pages 247-268

  16. Classifying Modules in Add of a Class of Modules with Semilocal Endomorphism Rings

    • Pavel Příhoda
    Pages 269-282

  17. The Multiplicative Ideal Theory of Leavitt Path Algebras of Directed Graphs—A Survey

    • Kulumani M. Rangaswamy
    Pages 283-297

  18. When Two Principal Star Operations Are the Same

    • Dario Spirito
    Pages 299-315

  19. Tilting Modules and Tilting Torsion Pairs

    • Francesco Mattiello, Sergio Pavon, Alberto Tonolo
    Pages 317-339
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  1. Advances in Rings, Modules and Factorizations

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About this book

Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra.  A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches. 





Editors and Affiliations

  • Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padua, Italy

    Alberto Facchini

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

    Marco Fontana

  • Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Graz, Austria

    Alfred Geroldinger

  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

    Bruce Olberding

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