Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups

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.

List 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.

Summary

Offers a new, universal algebraic and lattice-theoretical approach Provides tools for further work, for example on varieties of algebras, but also on operator theory Includes many examples and counterexamples

Product details

• Authors: Friedrich Wehrung
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 31.10.2017
• EAN: 9783319615981
• ISBN: 978-3-31-961598-1
• No. of pages: 242
• Dimensions: 156 mm x 17 mm x 238 mm
• Weight: 409 g
• Illustrations: VII, 242 p. 5 illus.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, B, Algebraische Topologie, Integralrechnung und -gleichungen, measure theory, Group Theory, Mathematics and Statistics, Rings (Algebra), Group Theory and Generalizations, Integral calculus & equations, Algebraic Topology, Measure and Integration, Associative rings, Associative Rings and Algebras, Order, Lattices, Ordered Algebraic Structures, Ordered algebraic structures, General Algebraic Systems, K-Theory