Ideal Theoretic Methods in Commutative Algebra

by Anderson; Daniel

• ISBN13: 9780824705534
• ISBN10: 082470553X
• eBook ISBN(s): 9780429530449
• Format: Nonspecific Binding
• Copyright: 2001-05-04
• Publisher: CRC Press
• More Book Details

Summary

Includes current work of 38 renowned contributors that details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. Summarizes recent findings on classes of going-down domains and the going-down property, emphasizing new characterizations and applications, as well as generalizations for commutative rings with zero divisors.

Table of Contents

Preface	iii
Contributors	vii
F-Rational Rings and the Integral Closures of Ideals II	1	(12)
Ian M. Aberbach
Craig Huneke
Cancellation Modules and Related Modules	13	(14)
D. D. Anderson
Abstract Ideal Theory from Krull to the Present	27	(22)
D. D. Anderson
E. W. Johnson
Conditions Equivalent to Seminormality in Certain Classes of Commutative Rings	49	(12)
David F. Anderson
Ayman Badawi
The Zero-Divisor Graph of a Commutative Ring, II	61	(12)
David F. Anderson
Andera Frazier
Aaron Lauve
Philip S. Livingston
Some Examples of Locally Divided Rings	73	(12)
Ayman Badawi
David E. Dobbs
On the Dimension of the Jacquet Module of a Certain Induced Representation	85	(4)
William Banks
Daniel Bump
Daniel Lieman
m-Canonical Ideals in Integral Domains II	89	(20)
Valentina Barucci
Evan Houston
Thomas G. Lucas
Ira J. Papick
The T-and v-Spectra of the Ring of Integer-Valued Polynomials Over a Valuation Domain	109	(10)
Paul-Jean Cahen
Evan Houston
Francesca Tartarone
Weakly Factorial Rings with Zero Divisors	119	(14)
Gyu Whan Chang
Equivalence Classes of Minimal Zero-Sequences Modulo a Prime	133	(14)
Scott T. Chapman
Michael Freeze
William W. Smith
Towards a Criterion for Isomorphisms of Complexes	147	(8)
S. Dale Cutkosky
Hema Srinivasan
Ideals Having a One-Dimensional Fiber Cone	155	(16)
Marco D' Anna
Anna Guerrieri
William Heinzer
Recent Progress on Going-Down II	171	(18)
David E. Dobbs
Kronecker Function Rings: A General Approach	189	(18)
Marco Fontana
K. Alan Loper
On the Complete Integral Closure of the Rees Algebra	207	(16)
Stefania Gabelli
Anna Guerrieri
A New Criterion for Embeddability in a Zero-Dimensional Commutative Ring	223	(8)
Robert Gilmer
Finite Conductor Properties of R(X) and R>X<	231	(20)
Sarah Glaz
Building Noetherian and Non-Noetherian Integral Domains Using Power Series	251	(14)
William Heinzer
Christel Rotthaus
Sylvia Wiegand
Integrality Properties in Rings with Zero Divisors	265	(16)
Thomas G. Lucas
Prime-Producing Cubic Polynomials	281	(38)
Joe L. Mott
Kermit Rose
Stability of Ideals and Its Applications	319	(24)
Bruce Olberding
Categorically Domains: Highlighting the (Domain) Work of James A. Huckaba	343	(14)
Ira J. Papick
Index	357