Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

by Friedrich Wehrung
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eBook

Publisher: Springer International Publishing

Series: Lecture Notes in Mathematics

Publication Date: October 08, 2017

ISBN: 9783319615998

Binding: Kobo eBook

Availability: eBook

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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.