Zero-Dimensional Commutative Rings: Proceedings of the 1994 John H. Barrett Memorial Lectures and Conference on Commutative Ring Theory

Zero-Dimensional Commutative Rings: Proceedings of the 1994 John H. Barrett Memorial Lectures and Conference on Commutative Ring Theory

by David F. Anderson
     
 

ISBN-10: 0824796055

ISBN-13: 9780824796051

Pub. Date: 04/10/1995

Publisher: Taylor & Francis

This work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature, and offers a comprehensive index for easy access to information. Wide-ranging developments in commutative ring theory are examined.

Overview

This work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature, and offers a comprehensive index for easy access to information. Wide-ranging developments in commutative ring theory are examined.

Product Details

ISBN-13:
9780824796051
Publisher:
Taylor & Francis
Publication date:
04/10/1995
Series:
Lecture Notes in Pure and Applied Mathematics Series, #171
Edition description:
New Edition
Pages:
400
Product dimensions:
6.25(w) x 9.25(h) x 0.50(d)

Related Subjects

Table of Contents

Background and preliminaries on zero-dimensional rings; zero-dimensionality and products of commutative rings; zero-dimensional extension rings and subrings; residue fields of zero-dimensional rings; dimensions of extension rings; Picard groups, cancellation and the multiplicative structure of fields; derivations and deformations of zero-dimensional rings and algebras; the ring R[X,r/X]; P.M. Cohn's completely primal elements; some factorization properties of the ring of integer-valued polynomials; on the nonuniversality of weak normalization; a visit to valuation and pseudo-valuation domains; answer to a question on the principal idea theorem; on the Davenport constant, the cross number, and their application in factorization theory; the Picard group of a polynomial ring; integral extensions with fibers of prescribed cardinality; homological dimensions of localizations of polynomial rings; splitting rings for p-local torsion-free groups; prime ideals in birational extensions of polynomial rings II; duals of ideals in pullback constructions; cancellation and prime spectra; the ascending chain condition on n-generated submodules; more almost Dedekind domains and Prufer domains of polynomials; direct limits of finite products of fields; Eisenstein-type irreducibility criteria; on integer-valued polynomials; the prime spectrum of an infinite product of zero dimensional rings; when is a self-injective ring zero-dimensional?; some problems in commutative ring theory.

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