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Record Nr. |
UNISA996466541403316 |
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Autore |
Wehrung Friedrich |
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Titolo |
Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups [[electronic resource] /] / by Friedrich Wehrung |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
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ISBN |
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Edizione |
[1st ed. 2017.] |
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Descrizione fisica |
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1 online resource (VII, 242 p. 5 illus.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 2188 |
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Disciplina |
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Soggetti |
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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 |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of |
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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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