Noncommutative Localization in Algebra and Topology

by Andrew Ranicki (Editor)

Overview

Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P.M. Cohn) it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry.This volume consists of 9 articles on noncommutative localization in algebra and topology. The aricles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material.

Product Details

ISBN-13:	9780521681605
Publisher:	Cambridge University Press
Publication date:	02/09/2006
Series:	London Mathematical Society Lecture Note Series , #330
Edition description:	First Edition
Pages:	328
Product dimensions:	5.98(w) x 9.06(h) x 0.75(d)

About the Author

Andrew Ranicki is a Professor of Algebraic Surgery, at the School of Mathematics, University of Edinburgh.

Table of Contents

Dedication; Preface; Historical perspective; Conference participants; Conference photo; Conference timetable; 1. On flatness and the Ore condition J. A. Beachy; 2. Localization in general rings, a historical survey P. M. Cohn; 3. Noncommutative localization in homotopy theory W. G. Dwyer; 4. Noncommutative localization in group rings P. A. Linnell; 5. A non-commutative generalisation of Thomason's localisation theorem A. Neeman; 6. Noncommutative localization in topology A. A. Ranicki; 7. L2-Betti numbers, isomorphism conjectures and noncommutative localization H. Reich; 8. Invariants of boundary link cobordism II. The Blanchfield-Duval form D. Sheiham; 9. Noncommutative localization in noncommutative geometry Z. Skoda.