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Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

  • Friedrich Wehrung

Part of the Lecture Notes in Mathematics book series (LNM, volume 2188)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Friedrich Wehrung
    Pages 1-22
  3. Friedrich Wehrung
    Pages 23-69
  4. Friedrich Wehrung
    Pages 109-147
  5. Friedrich Wehrung
    Pages 221-224
  6. Back Matter
    Pages 225-242

About this book

Introduction

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.

Keywords

Additive homomorphism Bias Boolean Commutative Distributive Equidecomposable Inverse Refinement Monoid Semigroup V-measure

Authors and affiliations

  • Friedrich Wehrung
    • 1
  1. 1.Département de MathématiquesUniversité de Caen NormandieCaenFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-61599-8
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-61598-1
  • Online ISBN 978-3-319-61599-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site