Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups [electronic resource] / by Friedrich Wehrung.

By:

Wehrung, Friedrich [author.]

Contributor(s):

SpringerLink (Online service)

Material type: Text

TextSeries: Lecture Notes in Mathematics ; 2188Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Description: VII, 242 p. 5 illus. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783319615998

Subject(s):

Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:

512.2 23

LOC classification:

QA174-183

Online resources:

Click here to access online

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.

In: Springer eBooksSummary: 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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