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Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups
Friedrich Wehrung
出版Springer, 2017-09-09
主題Mathematics / Algebra / AbstractMathematics / Mathematical AnalysisMathematics / Group TheoryMathematics / Algebra / GeneralMathematics / TopologyMathematics / Calculus
ISBN33196159989783319615998
URLhttp://books.google.com.hk/books?id=rc40DwAAQBAJ&hl=&source=gbs_api
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註釋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.