Screen LibraryRefinement 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...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
Springer International Publishing : Imprint: Springer,
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| Publisher Address: | Cham : |
| Publication Dates: | 2017. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Lecture Notes in Mathematics,
2188 |
| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1007/978-3-319-61599-8 |
| Summary: |
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. |
| Carrier Form: | 1 online resource (VII, 242 pages): illustrations. |
| ISBN: | 9783319615998 |
| Index Number: | QA174 |
| CLC: | O152 |
| 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. |