Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Algebra
Cover of the book Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups by Friedrich Wehrung, Springer International Publishing
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Author: Friedrich Wehrung ISBN: 9783319615998
Publisher: Springer International Publishing Publication: September 9, 2017
Imprint: Springer Language: English
Author: Friedrich Wehrung
ISBN: 9783319615998
Publisher: Springer International Publishing
Publication: September 9, 2017
Imprint: Springer
Language: English

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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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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