Ideal Theoretic Methods in Commutative Algebra: 1st Edition (Paperback) book cover

Ideal Theoretic Methods in Commutative Algebra

1st Edition

Edited by Daniel Anderson, Ira J. Patrick

CRC Press

294 pages

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Paperback: 9780824705534
pub: 2001-05-04

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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.

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.

About the Series

Lecture Notes in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Algebra / General