Recent Progress in Ring and Factorization Theory
Description
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 Bresar 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.
More details
Other editions
Additional editions
Persons
Matej Bresar received his PhD from the University of Ljubljana in 1990 and is currently Professor of Mathematics at the University of Ljubljana and the University of Maribor. His research focus lies in noncommutative algebra and its applications. He is the author or co-author of approximately 170 research papers and four books (two textbooks and two research monographs) published by Springer. He serves as an editor for Linear Algebra and its Applications and Mediterranean Journal of Mathematics.
Alfred Geroldinger received his PhD from the University of Graz in 1987 and is currently Professor of Mathematics at the University of Graz (Austria). He has published approximately 120 research papers in commutative algebra and additive combinatorics. He has served as co-organizer of conferences in ring theory, factorization theory, and additive combinatorics. He serves as an editor for the Communications in Algebra, the Communications of the Korean Mathematical Society, and the Korean Journal of Mathematics.
Bruce Olberding received his PhD from Wesleyan University in 1996 and is currently Professor of Mathematics at New Mexico State University. He has published approximately 90 research articles, mostly in commutative algebra, and he has spoken at a number of domestic and international conferences. He has served as co-organizer of conferences in commutative ring theory and factorization theory. He has co-edited five books, including four published by Springer. He serves as an editor for the Journal of Commutative Algebra and the Journal of Algebra and its Applications.
Daniel Smertnig obtained his PhD at the University of Graz in 2014, and had stops at Dartmouth College and the University of Waterloo as a postdoc before joining the University of Ljubljana as Associate Professor in 2023. His research focus is in noncommutative ring theory and factorization theory, and he has coorganized and participated in a number of international conferences on ring theory and ideal theory. He is an editor of the Communications of the Korean Mathematical Society.
Content
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.