E-Book, Englisch, 392 Seiten, Web PDF
Blyth / Janowitz / Sneddon Residuation Theory
1. Auflage 2014
ISBN: 978-1-4831-5714-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 392 Seiten, Web PDF
Reihe: International Series in Pure and Applied Mathematics
ISBN: 978-1-4831-5714-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Residuation Theory aims to contribute to literature in the field of ordered algebraic structures, especially on the subject of residual mappings. The book is divided into three chapters. Chapter 1 focuses on ordered sets; directed sets; semilattices; lattices; and complete lattices. Chapter 2 tackles Baer rings; Baer semigroups; Foulis semigroups; residual mappings; the notion of involution; and Boolean algebras. Chapter 3 covers residuated groupoids and semigroups; group homomorphic and isotone homomorphic Boolean images of ordered semigroups; Dubreil-Jacotin and Brouwer semigroups; and lolimorphisms. The book is a self-contained and unified introduction to residual mappings and its related concepts. It is applicable as a textbook and reference book for mathematicians who plan to learn more about the subject.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover ;1
2;Residuation Theory
;4
3;Copyright Page;5
4;Table of contents
;6
5;PREFACE;8
6;CHAPTER 1. FOUNDATIONS;12
6.1;1. Ordered sets;12
6.2;2. Mappings between ordered sets; residuated mappings;16
6.3;3. Directed sets; semilattices;30
6.4;4. Lattices; complete lattices;38
6.5;5. Morphisms;47
6.6;6. Regular equivalences on an ordered set;52
6.7;7. Complementation in lattices;74
6.8;8. Modularity in lattices;82
6.9;9. Distributive lattices;86
6.10;10. Congruence relations;92
7;CHAPTER 2. COORDINATIZING BAER SEMIGROUPS
;105
7.1;11. Baer rings;105
7.2;12. Baer semigroups;115
7.3;13. Range-closed residuated mappings;129
7.4;14. Strongly regular Baer semigroups;146
7.5;15. Decreasing Baer semigroups;154
7.6;16. Annihilator-preserving homomorphisms;160
7.7;17. The notion of involution;172
7.8;18. Orthomodular lattices;178
7.9;19. Foulis semigroups;194
7.10;20. Idempotent residuated mappings;200
7.11;21. Boolean algebras;210
8;CHAPTER 3. RESIDUATED ALGEBRAIC STRUCTURES;222
8.1;22. Residuated groupoids and semigroups; Molinaro equivalences;222
8.2;23. The zigzag equivalence;238
8.3;24. Group homomorphic images of ordered semigroups; Querré semigroups;258
8.4;25. Dubreil-Jacotin semigroups; A-nomal semigroups;271
8.5;26· Particular types of A-nomal semigroups;293
8.6;27. F-nomality;302
8.7;28. B-nomality
;311
8.8;29. Isotone homomorphic Boolean images of ordered semigroups;320
8.9;30. Glivenko semigroups;332
8.10;31. Loipomorphisms;342
8.11;32. Brouwer semigroups; Brouwer semilattices;351
9;BIBLIOGRAPHY;372
10;INDEX;384
11;OTHER TITLES IN THE SERIES IN PUREAND APPLIED MATHEMATICS;391
