Non-Noetherian Commutative Ring Theory

by Chapman, Scott T.; Glaz, Sarah

• ISBN13: 9780792364924
• ISBN10: 0792364929
• Format: Hardcover
• Copyright: 2000-10-01
• Publisher: Kluwer Academic Pub

Summary

This volume consists of twenty-one articles by many of the most prominent researchers in non-Noetherian commutative ring theory. The articles combine in various degrees surveys of past results, recent results that have never before seen print, open problems, and an extensive bibliography. One hundred open problems supplied by the authors have been collected in the volume's concluding chapter. The entire collection provides a comprehensive survey of the development of the field over the last ten years and points to future directions of research in the area. Audience: Researchers and graduate students; the volume is an appropriate source of material for several semester-long graduate-level seminars and courses.

Table of Contents

Preface	ix
GCD Domains, Gauss' Lemma, and Contents of Polynomials	1	(32)
D.D. Anderson
The Class Group and Local Class Group of an Integral Domain	33	(24)
David F. Anderson
Mori Domains	57	(18)
Valentina Barucci
What's New About Integer-Valued Polynomials on a Subset?	75	(22)
Paul-Jean Cahen
Jean-Luc Chabert
Half-Factorial Domains, a Survey	97	(20)
Scott T. Chapman
Jim Coykendall
On Generalized Lengths of Factorizations in Dedekind and Krull Domains	117	(22)
Scott T. Chapman
Michael Freeze
William W. Smith
Recent Progress on Going-Down I	139	(30)
David E. Dobbs
Localizing Systems and Semistar Operations	169	(30)
Marco Fontana
James A. Huckaba
Ideal Theory in Pullbacks	199	(30)
Stefania Gabelli
Evan Houston
Commutative Rings of Dimension 0	229	(22)
Robert Gilmer
Finite Conductor Rings with Zero Divisors	251	(20)
Sarah Glaz
Construction of Ideal Systems with Nice Noetherian Properties	271	(16)
Franz Halter-Koch
Generalized Local Rings and Finite Generation of Powers of Ideals	287	(26)
William Heinzer
Moshe Roitman
Connecting Trace Properties	313	(12)
James A. Huckaba
Ira Papick
Constructing Examples of Integral Domains by Intersecting Valuation Domains	325	(16)
K. Alan Loper
Examples Built With D+M, A+XB[X] and Other Pullback Constructions	341	(28)
Thomas G. Lucas
T-Closedness	369	(18)
Gabriel Picavet
Martine Picavet-L'Hermitte
E-rings and Related Structures	387	(16)
C. Vinsonhaler
Prime Ideals and Decompositions of Modules	403	(26)
Roger Wiegand
Sylvia Wiegand
Putting t-Invertibility to Use	429	(30)
Muhammad Zafrullah
One Hundred Problems in Commutative Ring Theory	459	(18)
Scott T. Chapman
Sarah Glaz
Index	477