Noncommutative Localization in Algebra and TopologyAndrew Ranicki Cambridge University Press, 9 feb 2006 - 313 páginas 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 by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles 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. It is suitable for graduate students and more advanced researchers in both algebra and topology. |
Índice
On flatness and the Ore condition | 1 |
Noncommutative localization in homotopy theory | 24 |
Noncommutative localization in group rings | 40 |
A noncommutative generalisation of Thomasons localisation theorem | 60 |
Noncommutative localization in topology | 81 |
Términos y frases comunes
abelian category algebraic geometry algebraic K-theory boundary link chain complex cobordism cofibre Cohn localization colimit comonad Conjecture construction Corollary defined definition denote dimr division ring domain duality-preserving functor element embedding endomorphism equation equivalence exact sequence example F-link f-local filtered finite subgroups finitely generated projective finitely presented Flk(A Flk(k free group full subcategory given group ring hence hermitian categories homology homotopy ideal implies induces injective invariants invertible involution kernel L2-Betti numbers left Ore condition left R-module Math matrix ring monad monoidal morphism multiplicative natural isomorphism natural transformation Neumann regular noncommutative localization objects pair primitive modules Proof Proposition quasideterminants quotient R-module Ranicki ring homomorphism S-¹R satisfies Sei(A Seifert forms Seifert module Seifert surface sheaves spaces submodule subring subset Suppose Theorem theory Thomason's topology torsion unique universal localization V[Fµ Vect/X vector bundles von Neumann algebras Waldhausen Witt groups