A Course in Constructive Algebra
The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bish
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F.W. Gehring P.R. Halmos
Universitext Editors: J. Ewing . F.W. Gehring. and P.R. Halmos
Booss/Bleecker: Topology and Analysis Charlap: Bieberbach Groups and Flat Manifolds Chern: Complex Manifolds Without Potential Theory Chorin/Marsden: A Mathematical Introduction to Fluid Mechanics Cohn: A Classical Invitation to Algebraic Numbers and Class Fields Curtis: Matrix Groups. 2nd ed. van Dalen: Logic and Structure Devlin: Fundamentals of Contemporary Set Theory Edwards: A Formal Background to Mathematics I a l b Edwards: A Formal Background to Mathematics II al b Endler: Valuation Theory Frauenthal: Mathematical Modeling in Epidemiology Gardiner: A First Course in Group Theory Godbillon: Dynamical Systems on Surfaces Greub: Multilinear Algebra Hermes: Introduction to Mathematical Logic Humi/Miller: Second Order Ordinary Differential Equations Hurwitz/Kritikos: Lectures on Number Theory Kelly/Matthews: The Non -Euclidean. The Hyperbolic Plane Kostrikin: Introduction to Algebra Luecking/Rubel: Complex Analysis: A Functional Analysis Approach Lu: Singularity Theory and an Introduction to Catastrophe Theory Marcus: Number Fields McCarthy: Introduction to Arithmetical Functions Mines/Richman/Ruitenburg: A Course in Constructive Algebra Meyer: Essential Mathematics for Applied Fields Moise: Introductory Problem Course in Analysis and Topology 0ksendal: Stochastic Differential Equations Porter/Woods: Extensions of Hausdorff Spaces Rees: Notes on Geometry Reisel: Elementary Theory of Metric Spaces Rey: Introduction to Robust and Quasi-Robust Statistical Methods Rickart: Natural Function Algebras Smith: Power Series From a Computational Point of View Smorynski: Self-Reference and Modal Logic StanisiC: The Mathematical Theory of Turbulence Stroock: An Introduction to the Theory of Large Deviations Sunder: An Invitation to von Neumann Algebras Tolle: Optimization Methods
Ray Mines Fred Richman Wim Ruitenburg
A Course in Constructive Algebra
Springer Science+Business Media, LLC
RayMines Fred Richman Department of Mathematical Sciences New Mexico State University Las Cruces. NM 88003 U.s.A
Wim Ruitenburg Department of Mathematics. Statistics, and Computer Science Marquette University Milwaukee, Wl 53233 U.s.A
AMS Classification: 03F65, 13-01
Library of Congress Cataloging-in-Publication Data Mines. Ray. A course in constructive algebra. (Universitext) Bibliography: p. Includes index. 1. Algebra 1. Richman. Fred. H. Ruitenburg, IV. Title: Constructive algebra. Wim. III. Title. QA155.M53 1988 512 87-26658
rtJ 1988 by Springer Science+Business Media New York Originally published by Springer-Ver lag New York Berlin Heidelberg in 1988 All right reserved. Thi, work may not be translated or copied in whole or in part without the written pennission ofthe publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. U se in cennection with any fonn of infonnation storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodolog
