Overview

This monograph is devoted to Krull domains and its invariants. The book shows how a serious study of invariants of Krull domains necessitates input from various fields of mathematics, including rings and module theory, commutative algebra, K-theory, cohomology theory, localization theory and algebraic geometry. About half of the book is dedicated to so-called involutive invariants, such as the involutive Brauer group. The work presents a large quantity of results previously scattered throughout the literature. This volume is a first introduction to this rapidly developing subject, but will also be useful as a reference work, both to students at graduate and postgraduate levels and to researchers in commutative rings and algebra, algebraic K-theory, algebraic geometry, and associative rings.

Full Product Details

Author:   M.V. Reyes Sánchez ,  A. Verschoren
Publisher:   Springer
Imprint:   Springer
Edition:   1999 ed.
Volume:   5
Dimensions:   Width: 16.00cm , Height: 1.70cm , Length: 24.00cm
Weight:   0.595kg
ISBN:  

9780792357193

ISBN 10:   0792357191
Pages:   260
Publication Date:   31 July 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Krull domains and their modules.- 1.1 Krull domains.- 1.2 Lattices.- 1.3 Divisorial lattices.- 1.4 The modified tensor product.- 1.5 A torsion-theoretic point of view.- 2. Classical invariants.- 2.1 The class group.- 2.2 The Brauer group.- 2.3 Enters cohomology.- 2.4 The long exact sequence.- 2.5 A K-theoretic point of view.- 3 Involutions.- 3.1 The categories C*.- 3.2 Algebras with involution.- 3.3 Involutions of trivial Azumaya algebras.- 3.4 Hermitian Picard groups.- 3.5 A Morita duality point of view.- 4 Involutive Brauer groups.- 4.1 Saltman’s theorem.- 4.2 The involutive Brauer group.- 4.3 Exact sequences.- 4.4 Cohomological interpretation.- 4.5 A geometric point of view.- 5 Functorial behaviour.- 5.1 Change of base ring.- 5.2 Divisorial descent.- 5.3 Separability and divisorial Galois theory.- 5.4 Norms.- 5.5 An Amitsur cohomology point of view.

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