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

By: Wehrung, Friedrich [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 2188Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Edition: 1st ed. 2017Description: VII, 242 p. 5 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319615998Subject(s): Group theory | Associative rings | Rings (Algebra) | Algebra | Ordered algebraic structures | K-theory | Measure theory | Group Theory and Generalizations | Associative Rings and Algebras | Order, Lattices, Ordered Algebraic Structures | General Algebraic Systems | K-Theory | Measure and IntegrationAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 512.2 LOC classification: QA174-183Online 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 Nature eBookSummary: 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.
Item type: E-BOOKS
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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.

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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