Rings, Polynomials, and Modules

This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016 : "Recent Advances in Commutative Ring and Module Theory, " Bressanone, Italy; "Conference on Rings and Polynomials" Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.-- Provided by publisher Front Matter ....Pages i-viii Reducing Fractions to Lowest Terms (Daniel D. Anderson, Erik Hasse)....Pages 1-11 Unique Factorization in Torsion-Free Modules (Gerhard Angermüller)....Pages 13-31 n-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey (Ayman Badawi)....Pages 33-52 Embedding Dimension and Codimension of Tensor Products of Algebras over a Field (S. Bouchiba, S. Kabbaj)....Pages 53-77 Minimal Generating Sets for the D-Algebra Int(S, D) (Jacques Boulanger, Jean-Luc Chabert)....Pages 79-101 Algebraic Entropy in Locally Linearly Compact Vector Spaces (Ilaria Castellano, Anna Giordano Bruno)....Pages 103-127 Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat (François Couchot)....Pages 129-143 Commutative Rings with a Prescribed Number of Isomorphism Classes of Minimal Ring Extensions (David E. Dobbs)....Pages 145-158 Applications of Multisymmetric Syzygies in Invariant Theory (M. Domokos)....Pages 159-174 Functorial Properties of Star Operations: New Developments (Jesse Elliott)....Pages 175-190 Systems of Sets of Lengths: Transfer Krull Monoids Versus Weakly Krull Monoids (Alfred Geroldinger, Wolfgang A. Schmid, Qinghai Zhong)....Pages 191-235 Corner’s Realization Theorems from the Viewpoint of Algebraic Entropy (Brendan Goldsmith, Luigi Salce)....Pages 237-255 Directed Unions of Local Quadratic Transforms of Regular Local Rings and Pullbacks (Lorenzo Guerrieri, William Heinzer, Bruce Olberding, Matthew Toeniskoetter)....Pages 257-280 Divisorial Prime Ideals in Prüfer Domains (Thomas G. Lucas)....Pages 281-298 A gg-Cancellative Semistar Operation on an Integral Domain Need Not Be gh-Cancellative (Ryûki Matsuda)....Pages 299-305 Quasi-Prüfer Extensions of Rings (Gabriel Picavet, Martine Picavet-L’Hermitte)....Pages 307-336 A Note on Analytically Irreducible Domains (Roswitha Rissner)....Pages 337-352 Integer-Valued Polynomials on Algebras: A Survey of Recent Results and Open Questions (Nicholas J. Werner)....Pages 353-375