This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principalideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory ortopology is assumed. Within the context of linear algebra, K-theory organisesand clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity andBrauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekinddomains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; thenecessary background is here, with proofs. INDICE: 1. Groups of modules: Ko; 2. Sources of Ko; 3. Groups of matrices:K1; 4. Relations among matrices: K2; 5. Sources of K2.
- ISBN: 978-0-521-10658-0
- Editorial: Cambridge University
- Encuadernacion: Rústica
- Páginas: 692
- Fecha Publicación: 04/02/2010
- Nº Volúmenes: 1
- Idioma: Inglés
- Inicio /
- MATEMÁTICAS /
- ÁLGEBRA