Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years.  Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals.  Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well.

Mathematics --- Number theory --- Ordered algebraic structures --- Algebra --- Algebraic geometry --- Geometry --- algebra --- landmeetkunde --- wiskunde --- getallenleer --- geometrie

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

Mathematics. --- Algebraic geometry. --- Associative rings. --- Rings (Algebra). --- Commutative algebra. --- Commutative rings. --- Group theory. --- Number theory. --- Commutative Rings and Algebras. --- Number Theory. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Algebraic Geometry. --- Factorization (Mathematics) --- Multiplicity (Mathematics) --- Multiplicity theory (Mathematics) --- Local rings --- Mathematics --- Algebra. --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Number study --- Numbers, Theory of --- Mathematical analysis --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)