This volume has been curated from two sources: presentations from the Conference on Rings and Polynomials, Technische Universität Graz, Graz, Austria, July 19 -24, 2021, and papers intended for presentation at the Fourth International Meeting on Integer-valued Polynomials and Related Topics, CIRM, Luminy, France, which was cancelled due to the pandemic. The collection ranges widely over the algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Two areas of particular note are topological methods in ring theory, and integer valued polynomials. The book is dedicated to the memory of Paul-Jean Cahen, a coauthor or research collaborator with some of the conference participants and a friend to many of the others. This collection contains a memorial article about Paul-Jean Cahen, written by his longtime research collaborator and coauthor Jean-Luc Chabert.
Table of Contents:
Paul-Jean Cahen (1946 – 2019) (Chabert).- Bhargava’s exponential functions and Bernoulli numbers associated to the set of prime numbers (Adam).- Polynomial root extensions (Anderson).- Absorbing ideals in commutative rings: A survey (Badawi).- Complement-finite ideals (Baeth).- When is a group algebra antimatter? (Baghdadi).- Yosida, Martínez, and A + B rings (Klingler).- Functional identities and maps preserving two-sided zero products (Brešar).- Bounded factorization and the ascending chain condition on principal ideals in generalized power series rings (Mooney).- Probabilities and fixed divisors of integer polynomials (Chabert).- Modules over trusses vs. modules over rings: Internal direct sums (Ferdania).- A survey on essential-like properties of Prüfer v--multiplication domains (Tartarone).- On the subatomicity of polynomial semidomains (Gotti).- Invertibility, semistar operations, and the ring of finite fractions (Juett).- The quadratic tree of a two-dimensional regular local ring (Olberding).- Reductions and core of ideals in integral domains: some recent developments (Kabbaj).- Valuative lattices and spectra (Lombardi).- Building 3-variable homogeneous integer-valued polynomials using generalized projective planes Marie MacDonald Around Prūfer extensions of rings (Picavet).- A survey on algebraic and homological properties of amalgamated algebras of commutative rings (Yassemi).- The ring of integer-valued polynomials on 3 × 3 matrices and its integral closure (Sodhi).- Simultaneous p-orderings and equidistribution (Szumowicz).- A survey on flatness in integer-valued polynomial rings (Tamoussit).- Equivalent characterizations of non-Archimedean uniform spaces (Windisch).
About the Author :
Jean-Luc Chabert is emeritus professor of mathematics at the Université de Picardie-Jules Verne. His research interests include algebraic number theory, commutative algebra, and rings of polynomials.
Marco Fontana is emeritus professor of algebra at the Università degli Studi "Roma Tre". His research interests lie in the areas of commutative ring theory and related topological aspects, with main focus on multiplicative ideal theory, Prüfer-like conditions and ideal factorizations, and Zariski-Riemann spaces of valuation domains.
Sophie Frisch is associate professor of mathematics at Technische Universität Graz, Graz, Austria. Her research interests are in commutative algebra and ring theory, including, but not limited to, polynomial mappings and integer-valued polynomials.
Sarah Glaz is emeritus professor of mathematics at the University of Connecticut. Her research interests lie in the areas of commutative ring theory and homological algebra, with main focus on non-Noetherian properties such as coherence, finite conductor, Gaussian, and Prüfer-like conditions of rings and their modules.
Keith Johnson is emeritus professor of mathematics at Dalhousie University. His research interests include number theory, algebraic topology and algebra, particularly the occurrence and uses of rings of integer valued polynomials in algebraic topology.
