Approximation Theorems in Commutative Algebra: Classical and Categorical Methods

by J. Alajbegovic, J. Mockor

Overview

Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc.
Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d-groups.
Part II investigates approximation theorems from a general, categorical point of view. This part is essentially self-contained and requires only a basic knowledge of category theory and first-order logic.
For researchers and graduate students of commutative algebra, category theory, as well as applications of logic.

Product Details

ISBN-13:	9789401052047
Publisher:	Springer Netherlands
Publication date:	11/05/2012
Series:	Mathematics and its Applications , #59
Edition description:	Softcover reprint of the original 1st ed. 1992
Pages:	330
Product dimensions:	6.30(w) x 9.45(h) x 0.03(d)

Table of Contents

I Classical Methods.- 1 Approximation Theorems For Valuations On Fields.- 2 Valuations On Commutative Rings.- 3 Ordered Groups And Homomorphisms.- 4 Approximation Theorems For Multi-Structures.- II Categorical Methods.- 5 Categorical Logic.- 6 Approximation Theorems In Categories.- Index of Notation.

Editorial Reviews

Various types of approximation theorems are frequently used in general commutative algebra, and are useful tools in valuation theory and Abelian lattice ordered groups. The first half of this volume investigates approximation theorems from a classical point of view and includes fields and rings, partially ordered groups, multirings, and d-groups. Part two examines approximation theorems from a general, categorical angle. It is self-contained and requires only a basic knowledge of category theory and first-order logic. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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