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＜電子ブック＞
Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups / by Friedrich Wehrung
(Lecture Notes in Mathematics. ISSN:16179692 ; 2188)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
大きさ	VII, 242 p. 5 illus : online resource
著者標目	*Wehrung, Friedrich author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Associative rings LCSH:Associative algebras LCSH:Algebra LCSH:Universal algebra LCSH:K-theory LCSH:Measure theory FREE:Group Theory and Generalizations FREE:Associative Rings and Algebras FREE:Order, Lattices, Ordered Algebraic Structures FREE:General Algebraic Systems FREE:K-Theory FREE:Measure and Integration
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-61599-8

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