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Full Description
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.
Contents
Preface.- 1 Reducing Fractions to Lowest Terms.- 2 Unique Factorization in Torsion-free Modules.- 3 n-Absorbing Ideals of Commutative Rings and Recent Progresses on Three Conjectures: A Survey.- 4 Embedding Dimension and Codimension of Tensor Products of Algebras Over a Field.- 5 Minimal Generating Sets for the D-Algebra Int(S,D).- 6 Algebraic Entropy in Locally Linearly Compact Vector Spaces.- 7 Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat.- 8 Commutative Rings with a Prescribed Number of Isomorphism Classes of Minimal Ring Extensions.- 9 Applications of Multisymmetric Syzygies in Invariant Theory.- 10 Functorial Properties of Star Operations: New Developments.- 11 Systems of Sets of Lengths: Transfer Krull Monoids Versus Weakly Krull Monoids.- 12 Corner’s Realization Theorems from the Viewpoint of Algebraic Entropy.- 13 Directed Unions of Local Quadratic Transforms of Regular Local Rings and Pullbacks.- 14 Divisorial Prime Ideals in PrüferDomains.- 15 A gg-Cancellative Semistar Operation on an Integral Domain Need Not Be gh-Cancellative.- 16 Quasi-Prüfer Extensions of Rings.- 17 A Note on Analytically Irreducible Domains.- 18 Integer-valued Polynomials on Algebras: A Survey of Recent Results and Open Questions.
