Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

1. Auflage 2017
ISBN: 978-3-319-61598-1
Verlag: Springer International Publishing

Buch, Englisch, Band 2188, 242 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 3869 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Wehrung, Friedrich

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

Chapter 1. Background.-  Chapter 2. Partial commutative monoids. -  Chapter 3. Boolean inverse semigroups and additive semigroup homorphisms.-  Chapter 4. Type monoids and V-measures. -  Chapter 5. Type theory of special classes of Boolean inverse semigroups. -  Chapter 6. Constructions involving involutary semirings and rings. - Chapter 7. discussion. - Bibliography.-  Author Index. - Glossary.- Index.