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Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups : Lecture Notes in Mathematics : Book 2188 - Friedrich Wehrung

Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

By: Friedrich Wehrung

eText | 9 September 2017

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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.

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