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Semigroups in Complete Lattices

✍ Scribed by Patrik Eklund, Javier Gutiérrez García, Ulrich Höhle, Jari Kortelainen

Publisher
Springer International Publishing
Year
2018
Tongue
English
Leaves
343
Series
Developments in Mathematics 54
Edition
1st ed.
Category
Library
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✦ Synopsis

This monograph provides a modern introduction to the theory of quantales.

First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research.

This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.

✦ Table of Contents

Front Matter ....Pages i-xxi
Foundations (Patrik Eklund, Javier Gutiérrez García, Ulrich Höhle, Jari Kortelainen)....Pages 1-43
Fundamentals of Quantales (Patrik Eklund, Javier Gutiérrez García, Ulrich Höhle, Jari Kortelainen)....Pages 45-202
Module Theory in ({\mathtt {Sup}}) (Patrik Eklund, Javier Gutiérrez García, Ulrich Höhle, Jari Kortelainen)....Pages 203-288
Back Matter ....Pages 289-326

✦ Subjects

Mathematics; Order, Lattices, Ordered Algebraic Structures; Category Theory, Homological Algebra; Mathematical Logic and Formal Languages

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