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010   $a3-319-61599-8
024 7 $a10.1007/978-3-319-61599-8
035   $a(CKB)4100000000587415
035   $a(DE-He213)978-3-319-61599-8
035   $a(MiAaPQ)EBC6300789
035   $a(MiAaPQ)EBC5595557
035   $a(Au-PeEL)EBL5595557
035   $a(OCoLC)1003860146
035   $a(PPN)204533252
035   $a(EXLCZ)994100000000587415
100   $a20170909d2017      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aRefinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups /$fby Friedrich Wehrung
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (VII, 242 p. 5 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2188
311   $a3-319-61598-X 
327   $aChapter 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.
330   $aAdopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2188
606   $aGroup theory
606   $aAssociative rings
606   $aRings (Algebra)
606   $aAlgebra
606   $aOrdered algebraic structures
606   $aK-theory
606   $aMeasure theory
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124
606   $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X
606   $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
615  0$aGroup theory.
615  0$aAssociative rings.
615  0$aRings (Algebra).
615  0$aAlgebra.
615  0$aOrdered algebraic structures.
615  0$aK-theory.
615  0$aMeasure theory.
615 14$aGroup Theory and Generalizations.
615 24$aAssociative Rings and Algebras.
615 24$aOrder, Lattices, Ordered Algebraic Structures.
615 24$aGeneral Algebraic Systems.
615 24$aK-Theory.
615 24$aMeasure and Integration.
676   $a512.2
700   $aWehrung$b Friedrich$4aut$4http://id.loc.gov/vocabulary/relators/aut$0512591
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910257379803321
996   $aRefinement monoids, equidecomposability types, and Boolean inverse semigroups$91466433
997   $aUNINA