03915nam 22007695 450 991025737980332120200630231003.03-319-61599-810.1007/978-3-319-61599-8(CKB)4100000000587415(DE-He213)978-3-319-61599-8(MiAaPQ)EBC6300789(MiAaPQ)EBC5595557(Au-PeEL)EBL5595557(OCoLC)1003860146(PPN)204533252(EXLCZ)99410000000058741520170909d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierRefinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups /by Friedrich Wehrung1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (VII, 242 p. 5 illus.) Lecture Notes in Mathematics,0075-8434 ;21883-319-61598-X 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.Lecture Notes in Mathematics,0075-8434 ;2188Group theoryAssociative ringsRings (Algebra)AlgebraOrdered algebraic structuresK-theoryMeasure theoryGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Order, Lattices, Ordered Algebraic Structureshttps://scigraph.springernature.com/ontologies/product-market-codes/M11124General Algebraic Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/M1106XK-Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11086Measure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Group 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.512.2Wehrung Friedrichauthttp://id.loc.gov/vocabulary/relators/aut512591MiAaPQMiAaPQMiAaPQBOOK9910257379803321Refinement monoids, equidecomposability types, and Boolean inverse semigroups1466433UNINA