Recent Progress in Ring and Factorization Theory

Matej Brešar 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.

• 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.