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Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

  • Book
  • © 2017

Overview

  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (7 chapters)

Keywords

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.

Authors and Affiliations

  • Département de Mathématiques, Université de Caen Normandie, Caen, France

    Friedrich Wehrung

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