Residuation Theory
- 1st Edition - January 1, 1972
- Latest edition
- Authors: T. S. Blyth, M. F. Janowitz
- Editors: I. N. Sneddon, M. Stark
- Language: English
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… Read more
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.
Preface
Chapter 1 Foundations
1. Ordered Sets
2. Mappings between Ordered Sets; Residuated Mappings
3. Directed Sets; Semilattices
4. Lattices; Complete Lattices
5. Morphisms
6. Regular Equivalences on an Ordered Set
7. Complementation in Lattices
8. Modularity in Lattices
9. Distributive Lattices
10. Congruence Relations
Chapter 2 Coordinatizing Baer Semigroups
11. Baer Rings
12. Baer Semigroups
13. Range-Closed Residuated Mappings
14. Strongly Regular Baer Semigroups
15. Decreasing Baer Semigroups
16. Annihilator-Preserving Homomorphisms
17. The Notion of Involution
18. Orthomodular Lattices
19. Foulis Semigroups
20. Idempotent Residuated Mappings
21. Boolean Algebras
Chapter 3 Residuated Algebraic Structures
22. Residuated Groupoids and Semigroups; Molinaro Equivalences
23. The Zigzag Equivalence
24. Group Homomorphic Images of Ordered Semigroups; Querré Semigroups
25. Dubreil-Jacotin Semigroups; A-Nomal Semigroups
26. Particular Types of A-Nomal Semigroups
27. F-Nomality
28. B-Nomality
29. Isotone Homomorphic Boolean Images of Ordered Semigroups
30. Glivenko Semigroups
31. Loipomorphisms
32. Brouwer Semigroups; Brouwer Semilattices
Bibliography
Index
Other Titles in the Series
- Edition: 1
- Latest edition
- Published: January 1, 1972
- Language: English
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