Ideal Theoretic Methods in Commutative Algebra

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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.

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Editorial Reviews

This volume compiles research papers presented at the University of Missouri, Columbia conference. It includes current research that illustrates the diversity of thought in the field of commutative algebra, particularly multiplicative ideal theory. It also presents survey articles on abstract ideal theory, going down, stable domains, prime producing polynomials, and integrality properties in rings with zero divisors. Written by mathematicians representing institutions in the United States, Europe, Asia, and the Middle East, the papers investigate F-rational rings, ideals having one-dimensional fiber cones, and isomorphism of complexes. They also describe seminormality, cancellation modules, and m-canonical ideals. Annotation c. Book News, Inc., Portland, OR (
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Table of Contents

F-rational rings and the integral closures of ideals II; cancellation modules and related modules; abstract ideal theory from Krull to the present; conditions equivalent to seminormality in certain classes of commutative rings; the zero-divisor graph of a commutative ring, II; some examples of locally divided rings; on the dimension of the Jacquet module of a certain induced representation; m-canonical ideals in integral domains II; the t- and v-spectra of the ring of integer-valued polynomials; weakly factorial rings with zero divisors; equivalence classes of minimal zero-sequences modulo a prime; towards a criterion for isomorphisms of complexes; ideals having a one-dimensional fibre cone; recent progress on going-down II; Kronecker function rings -a general approach; on the complete integral closure of the Rees algebra; a new criterion for embeddability in a zero-dimensional commutative ring; finite conductor properties of R(X) and R; building Noetherian and non-Noetherian integral domains using power series; integrality properties in rings with zero divisors; prime-producing cubic polynomials; stability of ideals and its applications; categorically domains - highlighting the (domain) work of James A. Huckaba.

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