Rings and Polynomials

Algebraic, Arithmetic, and Topological Topics in Ring Theory
Erscheinungsjahr 2027
ISBN: 978-3-032-46190-2
Verlag: Springer International Publishing

Buch, Englisch, Format (B × H): 155 mm x 235 mm

This book presents a collection of original research articles and invited survey contributions arising from the conference on  held at Graz University of Technology in July 2025. Written by leading researchers and emerging scholars from around the world, the volume highlights recent advances and current directions in ring theory and its interactions with neighboring areas of mathematics. All contributions have undergone rigorous peer review, ensuring a high standard of originality, depth, and mathematical quality.
 
The topics covered span a broad spectrum of contemporary research, including algebraic, number-theoretic, and topological aspects of rings, algebras, and polynomial structures. Alongside specialized research papers, invited survey chapters provide valuable overviews of active and developing areas, making the volume an accessible entry point to important themes while also serving as a reference for experts. Together, the chapters reflect the vibrant exchange of ideas that characterizes modern research in algebra and its many connections across mathematics.
 
Published fifteen years after the inaugural Graz conference on ring theory, this volume also celebrates a thriving international community built through a longstanding series of meetings in the Alps-Adriatic region. The contributions bear witness to a tradition of collaboration, mentorship, and scholarly exchange that has connected mathematicians across generations and continents. As the conference series enters a new phase of leadership and growth, this book captures both the achievements of the field today and the promise of future developments.

Zielgruppe

Research

Autoren/Hrsg.

Finocchiaro, Carmelo Antonio

Frisch, Sophie

Peruginelli, Giulio

Rissner, Roswitha

Smertnig, Daniel

Tartarone, Francesca

Inhaltsverzeichnis

Chapter 1. Characterizations of locally finitely generated monoids.- Chapter 2. On dihedral invariants of the free associative algebra of rank two.- Chapter 3. Schur’s irreducibility theorem and Bhargava’s generalized factorials.- Chapter 4. The Cyclicity of Tensor Products of Cyclic -Algebras.- Chapter 5. Null Ideals of a Ring of Matrices.- Chapter 6. The separating Noether number of small groups.- Chapter 7. Central polynomials of minimal degree for matrices.- Chapter 8. An introduction to reciprocal complements of integral domains.- Chapter 9. The 3 Definitions of Digroups.- Chapter 10. The ring of copolynomials over the commutative ring and some of its applications.- Chapter 11. Coarse lower topologies on algebraic structures.- Chapter 12. Trace ideals and uniserial modules.- Chapter 13. On the radical power graphs of semigroups of homogeneous elements of graded rings.- Chapter 14. On local log-regular rings.- Chapter 15. Gorenstein Dedekind Domains and Their Generalizations: A Survey.- Chapter 16. N-Rings: Variations on an Example by Heinzer and Lantz.- Chapter 17. On the stabillity of certain semigroup domains.- Chapter 18. Generalized special sequences I.- Chapter 19. An introduction to the patch topology.- Chapter 20. Companion matrices as sums of -potent and nilpotent matrices.- Chapter 21. The Largest Possible Finite Degree of Functions Between Abelian Groups.- Chapter 22. Smooth sequences and overring operators.- Chapter 23. Applications of reduced and coreduced modules II: Radicality of the functor Hom(/, -).- Chapter 24. Polynomial Identity Rings Associated With Powers of Dedekind Eta-Function.

Über Autor(innen)

Carmelo Antonio Finocchiaro has been working at the University of Catania as a full professor since October 2026. He earned his PhD in Mathematics from Roma Tre University and held postdoctoral research positions at the Roma Tre University and at the University of Technology of Graz. He was an assistant professor at the University of Padua and at the University of Catania where he also served as an associate professor. The focus of his research is on commutative algebra with special emphasis on topological methods on ring theory and multiplicative ideal theory. 

Sophie Frisch is an associate professor of mathematics at Technische Universität Graz, Austria. Her research interests include commutative algebra and ring theory, including, but not limited to, polynomial mappings and integer-valued polynomials.

Giulio Peruginelli has been an associate professor at the Department of Mathematics in the University of Padova, Italy since 2020. He studied mathematics at the University of Pisa, where he received his PhD in 2008. His research interests include commutative algebra and algebraic number theory, with a particular focus on Prüfer domains and integrally closed domains between the polynomial rings Z[X] and Q[X].

Roswitha Rissner is a senior scientist at the University of Klagenfurt, Austria. Her research interest lie in commutative algebra and number theory including combinatorial and computational aspects.

Daniel Smertnig is an associate professor of mathematics at the University of Ljubljana and is affiliated with the Institute of Mathematics, Physics and Mechanics (IMFM). His research centers on the interplay of arithmetic properties and algebraic structures, with work in noncommutative ring theory, factorization theory, and weighted automata, as well as on rational, D-finite, and Mahler series.

Francesca Tartarone has been an associate professor of algebra at Roma Tre University since March 2008. She earned her PhD in Mathematics from Sapienza University of Rome and held postdoctoral positions at Aix-Marseille University, the University of Trieste, and Roma Tre University. She has participated in numerous international conferences and has published several articles in international journals. Her research interests lie in commutative algebra, with particular interest in integer-valued polynomial rings and multiplicative ideal theory.