Residuation Theory

Residuation Theory

1st Edition - January 1, 1972

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  • Authors: T. S. Blyth, M. F. Janowitz
  • eBook ISBN: 9781483157146

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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.

Table of Contents

  • 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



    Other Titles in the Series

Product details

  • No. of pages: 392
  • Language: English
  • Copyright: © Pergamon 1972
  • Published: January 1, 1972
  • Imprint: Pergamon
  • eBook ISBN: 9781483157146

About the Authors

T. S. Blyth

M. F. Janowitz

About the Editors

I. N. Sneddon

M. Stark

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