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Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups / by Friedrich Wehrung.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2366,2368-2379,2381-2382 2385,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Wehrung, Friedrich., Author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 2188
- Language:
- English
- Subjects (All):
- 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 Integration.
- Local Subjects:
- Group Theory and Generalizations.
- Associative Rings and Algebras.
- Order, Lattices, Ordered Algebraic Structures.
- General Algebraic Systems.
- K-Theory.
- Measure and Integration.
- Physical Description:
- 1 online resource (VII, 242 p. 5 illus.)
- Edition:
- 1st ed. 2017.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2017.
- 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.
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-319-61599-8
- OCLC:
- 1003860146
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