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Residuation Theory
1st Edition - January 1, 1972
Authors: T. S. Blyth, M. F. Janowitz
Editors: I. N. Sneddon, M. Stark
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 5 7 1 4 - 6
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
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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
- No. of pages: 392
- Language: English
- Published: January 1, 1972
- Imprint: Pergamon
- eBook ISBN: 9781483157146