02604nam a2200409 i 4500991003560849707536m o d cr cnu|||unuuu181019s2017 sz a ob 001 0 eng d9783319615998(electronic bk.)3319615998(electronic bk.)10.1007/978-3-319-61599-8doib14351936-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. MatematicaengAMS 20-01LC QA182Wehrung, Friedrich512591Refinement monoids, equidecomposability types, and Boolean inverse semigroups[e-book] /Friedrich WehrungCham, Switzerland :Springer,20171 online resource (vii, 242 pages) :illustrationstexttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture notes in mathematics,0075-8434 ;2188Includes bibliographical references and indexesChapter 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 ; IndexAdopting 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 providedSemigroupsPrinted edition:9783319615981https://link.springer.com/book/10.1007/978-3-319-61599-8An electronic book accessible through the World Wide Web.b1435193603-03-2219-10-18991003560849707536Hiram College INTERNETOhioLINK E-book Center c.1AVAILABLERefinement monoids, equidecomposability types, and Boolean inverse semigroups1466433UNISALENTOle01319-10-18m@ -engsz 00