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This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. 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 as well as integer-valued polynomials and functions. Specific topics include: ·    Homological dimensions of Prüfer-like rings ·    Quasi complete rings ·    Total graphs of rings ·    Properties of prime ideals over various rings ·    Bases for integer-valued polynomials ·    Boolean subrings ·    The portable property of domains ·    Probabilistic topics in Intn(D) ·    Closure operations in Zariski-Riemann spaces of valuation domains ·    Stability of domains ·    Non-Noetherian grade ·    Homotopy in integer-valued polynomials ·    Localizations of global properties of rings ·    Topics in integral closure ·    Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.

Commutative algebra. --- Mathematics. --- Commutative rings. --- Algebraic topology. --- Algebra --- Topology --- Rings (Algebra) --- Math --- Science --- Algebra. --- Commutative Rings and Algebras. --- Category Theory, Homological Algebra. --- Algebraic Topology. --- Mathematics --- Mathematical analysis --- Category theory (Mathematics). --- Homological algebra. --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Functor theory

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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.

Mathematics. --- Associative rings. --- Rings (Algebra). --- Commutative algebra. --- Commutative rings. --- Commutative Rings and Algebras. --- Associative Rings and Algebras. --- Commutative rings --- Rings (Algebra) --- Algebra. --- Mathematics --- Mathematical analysis --- Algebraic rings --- Ring theory --- Algebraic fields --- Algebra

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This volume has been curated from two sources: presentations from the Conference on Rings and Polynomials, Technische Universität Graz, Graz, Austria, July 19 –24, 2021, and papers intended for presentation at the Fourth International Meeting on Integer-valued Polynomials and Related Topics, CIRM, Luminy, France, which was cancelled due to the pandemic. The collection ranges widely over the algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Two areas of particular note are topological methods in ring theory, and integer valued polynomials. The book is dedicated to the memory of Paul-Jean Cahen, a coauthor or research collaborator with some of the conference participants and a friend to many of the others. This collection contains a memorial article about Paul-Jean Cahen, written by his longtime research collaborator and coauthor Jean-Luc Chabert. .

Associative rings. --- Associative algebras. --- Commutative algebra. --- Commutative rings. --- Nonassociative rings. --- Associative Rings and Algebras. --- Commutative Rings and Algebras. --- Non-associative Rings and Algebras. --- Rings (Algebra) --- Algebra --- Algebras, Associative --- Anells (Àlgebra)