Rings, Polynomials, and Modules

Contributions cover areas in commutative algebra and related non-commutative generalizations that have flourished in the last few decades and are not yet well represented in book form

In addition to research articles, the volume provides comprehensive survey articles on recent advances and new trends in the field

The volume includes open problems that point to future directions of research

Auteur

Marco Fontana is 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, 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 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.

Francesca Tartarone is associate professor of algebra at the Università degli Studi "Roma Tre". Her research interests lie in the area of commutative ring theory with a particular focus on integer valued polynomial rings, star operations on ideals and multiplicative ideal theory properties of Prüfer-like domains.

Paolo Zanardo is professor of algebra at the Università di Padova. His research interests lie in the area of commutative rings and their modules, with main focus on modules over valuation domains, ideal class semigroups, algebraic entropies, fully inert Abelian Groups, and factorization of matrices over integral domains.

Contenu

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 Corners 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 Prüfer Domains.- 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.