Title: Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups (Lecture Notes in Mathematics, 2188)
Publisher: Springer
Publication Date: 2017
Language: English
ISBN 10: 331961598X
ISBN 13: 9783319615981
Binding: Soft cover
Condition: New

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Synopsis

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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