Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

• Main Author: Wehrung, Friedrich (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Lecture Notes in Mathematics, 2188
• Subjects: Mathematics.; Associative rings.; Rings (Algebra).; Algebra.; Group theory.; K-theory.; Ordered algebraic structures.; Measure theory.; Group Theory and Generalizations.; Associative Rings and Algebras.; Order, Lattices, Ordered Algebraic Structures.; General Algebraic Systems.; K-Theory.; Measure and Integration.
• Physical Description: VII, 242 p. 5 illus. online resource.
• ISBN: 9783319615998
• ISSN: 0075-8434 ;

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.