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Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

  • Offers a new, universal algebraic and lattice-theoretical approach

  • Provides tools for further work, for example on varieties of algebras, but also on operator theory

  • Includes many examples and counterexamples


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


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.


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

Authors and affiliations

  1. 1.Département de MathématiquesUniversité de Caen NormandieCaenFrance

Bibliographic information