TY  - BOOK
AU  - Wehrung,Friedrich
ED  - SpringerLink (Online service)
TI  - Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups
T2  - Lecture Notes in Mathematics,
SN  - 9783319615998
AV  - QA174-183 
U1  - 512.2 23
PY  - 2017///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Group theory
KW  - Associative rings
KW  - Rings (Algebra)
KW  - Algebra
KW  - Ordered algebraic structures
KW  - K-theory
KW  - Measure theory
KW  - Group Theory and Generalizations
KW  - Associative Rings and Algebras
KW  - Order, Lattices, Ordered Algebraic Structures
KW  - General Algebraic Systems
KW  - K-Theory
KW  - Measure and Integration
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-61599-8
ER  -