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Lattices and Ordered Algebraic Structures by Thomas S. Blyth
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About this book :-
Lattices and Ordered Algebraic Structures written by
Thomas S. Blyth .
The purpose of the present text is to provide a basic introduction to the theory of ordered structures. Taken as a whole, the material is mainly designed for a postgraduate course. However, since prerequisites are minimal, selected parts of it may easily be considered suitable to broaden the horizon of the advanced undergraduate. Indeed, this has been the author’s practice over many years.
A basic tool in analysis is the notion of a continuous function, namely a mapping which has the property that the inverse image of an open set is an open set. In the theory of ordered sets there is the corresponding concept of a residuated mapping, this being a mapping which has the property that the inverse image of a principal down-set is a principal down-set. It comes therefore as no surprise that residuated mappings are important as far as ordered structures are concerned. Indeed, albeit beyond the scope of the present exposition, the naturality of residuated mappings can perhaps best be exhibited using categorical concepts.
(Thomas S. Blyth)
Book Detail :-
Title: Lattices and Ordered Algebraic Structures
Edition:
Author(s): Thomas S. Blyth
Publisher: Springer
Series:
Year: 2005
Pages: 315
Type: PDF
Language: English
ISBN: 1852339055
Country: UK
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About Author :-
The author Thomas S. Blyth , University of St. Andrews, Scotland, UK. He is am an algebraist and have worked for the past forty years on algebraic structures that involve the notion of an order. My main interests fall into three areas, namely residuated mappings, algebraic and ordered semigroups, and Ockham algebras. As far as the first and third of these are concerned, I am coauthor of definitive research monographs on each. Other research publications include 120 papers in principal mathematical journals.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions, solution manuals or solved notes avaliable of this author, We recomended you to download all.
• Download PDF Sets and Mappings by Thomas S. Blyth, Edmund F. Robertson
• Download PDF Lattices and Ordered Algebraic Structures by Thomas S. Blyth
• Download PDF Groups by Thomas S. Blyth, Edmund F. Robertson
• Download PDF Residuation Theory by Thomas S. Blyth, Melvin F. Janowitz
• Download PDF Basic Linear Algebra by Thomas S. Blyth, Edmund F. Robertson
• Download PDF Basic Further Linear Algebra By Thomas S. Blyth, Edmund F. Robertson
• Download PDF Basic Matrices Vector Spaces by Thomas S. Blyth, Edmund F. Robertson
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Book Contents :-
Lattices and Ordered Algebraic Structures written by
Thomas S. Blyth
cover the following topics.
1. Ordered sets; residuated mappings
2. Lattices; lattice morphisms
3. Regular equivalences
4. Modular lattices
5. Distributive lattices
6. Complementation; boolean algebras
7. Pseudocomplementation; Stone and Heyting algebras
8. Congruences; subdirectly irreducible algebras
9. Ordered groups
10. Archimedean ordered structures
11. Ordered semigroups; residuated semigroups
12. Epimorphic group images; Dubreil-Jacotin semigroups
13. Ordered regular semigroups
14. Structure theorems
References
Index
Note:-
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