Commutative Algebra: Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions

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Marco Fontana, Sophie Frisch, Sarah Glaz
Springer, Jul 15, 2014 - Mathematics - 375 pages

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.


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Weak Global Dimension of PrüferLike Rings
Quasicomplete Semilocal Rings and Modules
A Survey
Prime Ideals in Polynomial and Power Series Rings over Noetherian Domains
Looking for Regular Bases A Survey
On Boolean Subrings of Rings
On a New Class of Integral Domains with the Portable Property
The Probability That IntnD Is Free
Stable Homotopy Theory Formal Group Laws and IntegerValued Polynomials
How to Construct Huge Chains of Prime Ideals in Power Series Rings
Localizing Global Properties to Individual Maximal Ideals
Prime Ideals That Satisfy Hensels Lemma
Finitely Stable Rings
Integral Closure of Rings of IntegerValued Polynomials on Algebras
On Monoids and Domains Whose Monadic Submonoids Are Krull
Integral Closure

A Survey
Ten Problems on Stability of Domains
The Development of NonNoetherian Grade and Its Applications
Open Problems in Commutative Ring Theory

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