Recent Progress in Ring and Factorization Theory

• Titel: Recent Progress in Ring and Factorization Theory
• Titelzusatz: Graz, Austria, July 10–14, 2023
• Mitwirkende: Brešar, Matej [HerausgeberIn]
• Mitwirkende: Geroldinger, Alfred [HerausgeberIn]
• Mitwirkende: Olberding, Bruce [HerausgeberIn]
• Mitwirkende: Smertnig, Daniel [HerausgeberIn]
• Körperschaft: Conference on Rings and Factorizations <2023, Graz> [VerfasserIn]
• Verf.angabe: edited by Matej Brešar, Alfred Geroldinger, Bruce Olberding, Daniel Smertnig
• Ausgabe: 1st ed. 2025.
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Jahr: 2025
• Umfang: 1 Online-Ressource(VIII, 450 p. 9 illus., 3 illus. in color.)
• Gesamttitel/Reihe: Springer Proceedings in Mathematics & Statistics ; 477
• ISBN: 978-3-031-75326-8
• DOI: doi:10.1007/978-3-031-75326-8
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Conference on Rings and Factorizations (2023 : Graz): Recent progress in ring and factorization theory. - Cham : Springer Nature Switzerland, 2025. - viii, 450 Seiten
• K10plus-PPN: 1925485870
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

The directed Cayley diameter and the Davenport constant -- Heaps and trusses -- Prüfer v-multiplication domains, a survey -- Some applications of a new approach to factorization -- Atomicity in integral domains -- Norms, normsets, and factorization.-On the Ratliff-Rush closure of an ideal of a one-dimensional ring -- Graded identities of infinite-dimensional Lie algebras.-On a class of quotients of Rees algebras: a survey -- P-adic approximation of algebraic integers and residue class rings of integer-valued polynomials -- On matrix superalgebras with pseudoautomorphism -- Krull Rings, Semistar Operations, and Bases of Regularity -- Descriptions of radicals in polynomial ring extensions -- Boolean inverse semigroups and their type monoids.-Generalized derivations characterized by their action on Jordan products -- Open problems on relations of numerical semigroups -- Irreducible integer-valued polynomials with prescribed minimal power that factors non-uniquely -- The role of divisors in non-commutative ideal theory -- Essential-like properties for integer-valued polynomial rings: a survey with a note on valuation domains -- On the isomorphism problem for power semigroups -- Dimension-free matricial Nullstellensätze for noncommutative polynomials.

Abstract

This proceedings volume gathers a selection of cutting-edge research in both commutative and non-commutative ring theory and factorization theory. The papers were presented at the Conference on Rings and Factorization held at the University of Graz, Austria, July 10–14, 2023. The volume covers a wide range of topics including multiplicative ideal theory, Dedekind, Prüfer, Krull, and Mori rings, non-commutative rings and algebras, rings of integer-valued polynomials, topological aspects in ring theory, factorization theory in rings and semigroups, and direct-sum decomposition of modules. The conference also featured two special sessions dedicated to Matej Brešar and Sophie Frisch on the occasion of their 60th birthdays. This volume is aimed at graduate students and researchers in these areas as well as related fields and provides new insights into both classical and contemporary research in ring and factorization theory.