Advances in Rings, Modules and Factorizations

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

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. 

• multiplicative ideal theory
• integer-valued polynomial
• monoid
• factorization
• commutative ring
• Prufer ring
• Krull ring
• Mori ring
• module
• ideal and module system
• star and semistar operation
• direct-sum decomposition
• sets of lengths
• arithmetical invariants

• 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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