Commutative ring theory and applications : proceedings of the fourth international conference

Featuring presentations from the Fourth International Conference held in Fez, Morocco. Emphasizes innovative applications and connections to algebraic number theory and geometry, and homological and computational algebra. 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 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, geome Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents recent breakthroughs and new trends in the growing area of commutative algebra emphasizing innovative applications and connections to algebraic number theory and geometry, and homological and computational algebra Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the area of commutative algebra. It emphasizes applications and connections to algebraic number theory, geometry, and homological and computational algebra.