Refinement Monoids Equidecomposability Types And Boolean Inverse Semigroups

Download or read book Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups written by Friedrich Wehrung and published by Springer. This book was released on 2017-09-09 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.