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Ideal Theoretic Methods in Commutative Algebra, in Honor of James A. Huckaba's Retirement

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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.

Author(s): Daniel D. Anderson; Ira J. Papick
Series: Lecture Notes In Pure And Applied Mathematics 220
Publisher: CRC Press
Year: 2019

Language: English
Pages: x+358

Cover
Half Title
Series Page
Lecture Notes In Pure And Applied Mathematics
Title Page
Copyright Page
Contents
Preface
Contributors
Chapter 1: F-Rational Rings and the Integral Closures of Ideals II
Chapter 2: Cancellation Modules and Related Modules
Chapter 3: Abstract Ideal Theory from Krull to the Present
Chapter 4: Conditions Equivalent to Seminormality in Certain Classes of Commutative Rings
Chapter 5: The Zero-Divisor Graph of a Commutative Ring, II
Chapter 6: Some Examples of Locally Divided Rings
Chapter 7: On the Dimension of the Jacquet Module of a Certain Induced Representation
Chapter 8: m-Canonical Ideals in Integral Domains II
Chapter 9: The t- and v-Spectra of the Ring of Integer-Valued Polynomials Over a Valuation Domain
Chapter 10: Weakly Factorial Rings with Zero Divisors
Chapter 11: Equivalence Classes of Minimal Zero-Sequences Modulo a Prime
Chapter 12: Towards a Criterion for Isomorphisms of Complexes
Chapter 13: Ideals Having a One-Dimensional Fiber Cone
Chapter 14: Recent Progress on Going-Down II
Chapter 15: Kronecker Function Rings: A General Approach
Chapter 16: On the Complete Integral Closure of the Rees Algebra
Chapter 17: A New Criterion for Embeddability in a Zero-Dimensional Commutative Ring
Chapter 18: Finite Conductor Properties of R(X) and R
Chapter 19: Building Noetherian and Non-Noetherian Integral Domains Using Power Series
Chapter 20: Integrality Properties in Rings with Zero Divisors
Chapter 21: Prime-Producing Cubic Polynomials
Chapter 22: Stability of Ideals and Its Applications
Chapter 23: Categorically Domains: Highlighting the (Domain) Work of James
Index