Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

by Friedrich Wehrung

Overview

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.

Product Details

ISBN-13:	9783319615981
Publisher:	Springer International Publishing
Publication date:	10/08/2017
Series:	Lecture Notes in Mathematics , #2188
Edition description:	1st ed. 2017
Pages:	242
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

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.