Titlebook: Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups; Friedrich Wehrung Book 2017 Springer International Publishi

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0075-8434 t also on operator theory.Includes many examples and counterAdopting 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-valu

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Book 2017of 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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0075-8434 igroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.978-3-319-61598-1978-3-319-61599-8Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Partial Commutative Monoids,l commutative monoid, which works then as the “enveloping monoid of .”. Although this process has been mostly studied in case . satisfies the refinement axiom (this originates in Tarski [109]), the initial part of the work does not require that axiom.

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Type Theory of Special Classes of Boolean Inverse Semigroups, in which the structure of . impacts greatly the one of .. A basic illustration of this is given by the class of ., introduced in Lawson and Scott [77], which is the Boolean inverse semigroup version of the class of AF C*-algebras. Another Boolean inverse semigroup version of a class of C*-algebras,

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