Commutative Ring Theory and Applications / Edition 1

by Marco Fontana, Salah-Eddine Kabbaj, Sylvia Wiegand

Overview

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.

Product Details

ISBN-13:	9781138401914
Publisher:	Taylor & Francis
Publication date:	07/27/2017
Series:	Lecture Notes in Pure and Applied Mathematics
Pages:	520
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

Marco Fontana, Salah-Eddine Kabbaj, Sylvia Wiegand

Table of Contents

Preface, Contributors, 1. D[X2, X3] Over an Integral Domain D, 2. On the Complete Integral Closure of Rings that Admit a <j)-Strongly Prime Ideal, 3. Frobenius Number of a Linear Diophantine Equation, 4. On Plane Algebroid Curves, 5. On Radical Operations, 6. A Splitting Property Characterizing Artinian Principal Ideal Rings, 7. Rings of Integer-Valued Polynomials and the bcs-Property, 8. Factorial Groups and Poly a Groups in Galoisian Extension of Q, 9. Monomial Ideals and the Computation of Multiplicities, 10. Analytic Spread of a Pregraduation, 11. Extension of the Hilbert-Samuel Theorem, 12. On the Integral Closure of Going-Down Rings, 13. Generalized Going-Down Homomorphisms of Commutative Rings, 14. The Class Group of the Composite Ring of a Pair of Krull Domains and Applications, 15. Complete Integral Closure and Noetherian Property for Integer- Valued Polynomial Rings, 16. Controlling the Zero Divisors of a Commutative Ring, 17. Weak Module Systems and Applications: A Multiplicative Theory of Integral Elements and the Marot Property, 18. Examples of Integral Domains Inside Power Series Rings, 19. Generalized Going-Up Homomorphisms of Commutative Rings, 20. Parameter-Like Sequences and Extensions of Tight Closure, 21. The Tor Game, 22. Trivial Extensions of Local Rings and a Conjecture of Costa, 23. On the t-Dimension of Integral Domains, 24. On Some Annihilator Conditions Over Commutative Rings, 25. On Projective Modules Over Polynomial Rings, 26. Rings, Conditional Expectations, and Localization, 27. Errata: Pullbacks and Coherent-Like Properties [In: Lect. Notes Pure Appl. Math., Dekker, 205 (1999) 437-459], 28. Ultraproducts of Commutative Rings, 29. Geometric Subsets of a Spectrum, 30. Trigonometric Polynomial Rings, 31. The First Mayr-Meyer Ideal, 32. Facets on Rings Between D[X] and K[X], 33. Constructions Cachees en Algebre Abstraites, 34. Hidden Constructions in Abstract Algebra: Krull Dimension of Distributive Lattices and Commutative Rings

Editorial Reviews

Material from a recent conference presents progress and trends in the area of commutative algebra, with emphasis on commutative ring theory and its applications, and on connections to algebraic number theory, algebraic geometry, homological algebra, and model-theoretic algebra. Topics covered include algebroid curves, arithmetic rings, chain conditions, class groups, construction of examples, and divisibility and factorization. Other subjects are linear Diophantine equations, the going-down and going-up properties, graded modules and analytic spread, Gröbner bases and computational methods, homological aspects of commutative rings, and Krull domains. Some chapters are surveys of their subject, while others present an in-depth view. There is no subject index. Annotation c. Book News, Inc., Portland, OR