Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geometry, and homological and computational algebra. Presenting challenging problems of contemporary interest, discussions include linear Diophantine equations, going-down and going-up properties, and graded modules and analytic spread. They also cover algebroid curves and chain conditions, ideals and modules, and integral independence.
Author(s): Marco Fontana, Salah-Eddine Kabbaj, Sylvia Wiegand
Series: Lecture Notes in Pure and Applied Mathematics
Edition: 1
Publisher: CRC Press
Year: 2002
Language: English
Pages: 517
Preface......Page 9
Contents......Page 11
Contributors......Page 15
D[X2, X3] Over an Integral Domain D......Page 19
On the Complete Integral Closure of Rings that Admit a (|)-Strongly Prime Ideal......Page 33
Frobenius Number of a Linear Diophantine Equation......Page 41
On Plane Algebroid Curves......Page 55
On Radical Operations......Page 69
A Splitting Property Characterizing Artinian Principal Ideal Rings......Page 79
Rings of Integer-Valued Polynomials and the bcs-Property......Page 83
Factorial Groups and Polya Groups in Galoisian Extension of Q......Page 95
Monomial Ideals and the Computation of Multiplicities......Page 105
Analytic Spread of a Pregraduation......Page 125
Extension of the Hilbert-Samuel Theorem......Page 135
On the Integral Closure of Going-Down Rings......Page 149
Generalized Going-Down Homomorphisms of Commutative Rings......Page 161
The Class Group of the Composite Ring of a Pair of Krull Domains and Applications......Page 183
Complete Integral Closure and Noetherian Property for Integer-Valued Polynomial Rings......Page 191
Controlling the Zero Divisors of a Commutative Ring......Page 209
Weak Module Systems and Applications: A Multiplicative Theory of Integral Elements and the Marot Property......Page 231
Examples of Integral Domains Inside Power Series Rings......Page 251
Generalized Going-Up Homomorphisms of Commutative Rings......Page 273
Parameter-Like Sequences and Extensions of Tight Closure......Page 285
The Tor Game......Page 307
Trivial Extensions of Local Rings and a Conjecture of Costa......Page 319
On the /-Dimension of Integral Domains......Page 331
On Some Annihilator Conditions Over Commutative Rings......Page 341
On Projective Modules Over Polynomial Rings......Page 353
Rings, Conditional Expectations, and Localization......Page 367
Errata: "Fullbacks and Coherent-Like Properties" [In: Lect. Notes Pure Appl. Math., Dekker, 205 (1999) 437-459]......Page 385
Ultraproducts of Commutative Rings......Page 387
Geometric Subsets of a Spectrum......Page 405
Trigonometric Polynomial Rings......Page 437
The First Mayr-Meyer Ideal......Page 453
Facets on Rings Between D[X] and K[X]......Page 463
Constructions Cachees en Algebre Abstraite: Le Principe Local-Global......Page 479
Hidden Constructions in Abstract Algebra: Krull Dimension of Distributive Lattices and Commutative Rings......Page 495
