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Residuation Theory - 1st Edition - ISBN: 9780080164083, 9781483157146

Residuation Theory

1st Edition

Authors: T. S. Blyth M. F. Janowitz
Editors: I. N. Sneddon M. Stark
eBook ISBN: 9781483157146
Imprint: Pergamon
Published Date: 1st January 1972
Page Count: 392
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Table of Contents


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



Other Titles in the Series


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.


No. of pages:
© Pergamon 1972
1st January 1972
eBook ISBN:

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About the Authors

T. S. Blyth

M. F. Janowitz

About the Editors

I. N. Sneddon

M. Stark