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

Front Cover
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.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Weak Global Dimension of PrüferLike Rings
1
Quasicomplete Semilocal Rings and Modules
25
A Survey
38
Prime Ideals in Polynomial and Power Series Rings over Noetherian Domains
55
Looking for Regular Bases A Survey
83
On Boolean Subrings of Rings
113
On a New Class of Integral Domains with the Portable Property
118
The Probability That IntnD Is Free
133
Stable Homotopy Theory Formal Group Laws and IntegerValued Polynomials
212
How to Construct Huge Chains of Prime Ideals in Power Series Rings
225
Localizing Global Properties to Individual Maximal Ideals
239
Prime Ideals That Satisfy Hensels Lemma
255
Finitely Stable Rings
269
Integral Closure of Rings of IntegerValued Polynomials on Algebras
292
On Monoids and Domains Whose Monadic Submonoids Are Krull
307
Integral Closure
331

A Survey
153
Ten Problems on Stability of Domains
174
The Development of NonNoetherian Grade and Its Applications
195
Open Problems in Commutative Ring Theory
352
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information