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Ockham Algebras By Thomas. S. Blyth, J. C. Varlet
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**About this book :- **

**Ockham Algebras** written by
** Thomas S. Blyth, J. C. Varlet **.

An Ockbam algebra is a bounded distributive lattice with a dual endomorphism, the nomenclature being chosen since the notion of de Morgan negation has been attributed to the logician William of Ockham (cI290-c1349). The class of such algebras is vast, containing in particular the well-known classes of boolean algebras, de Morgan algebras, Kleene algebras, and Stone algebras. Pioneering work by Berman in 1977 has shown the importance of Ockham algebras in general, and has since stimulated much research in this area, notably by Urquhart, Goldberg, Adams, Priestley, and Davey.

Here our objective is to provide a reasonably self-contained and readable account of some of this research. Our collaboration began in 1982 in the consideration of a common abstraction of de Morgan algebras and Stone algebras which we called MS-algebras. This class of Ockham algebras is characterised by the fact that the dual endomorphism] satisfies jO ~]2, which implies that ] =]3. The subvariety M of de Morgan algebras is characterised by]O =]2. In general, it seems an impossible task to describe all the subvarieties of Ockham algebras. The subvarieties of paramount importance are those in which]q =]2p+q for some p, q; these are denoted by Kp,q and are called the Berman varieties. Of these, the most significant seems to be K1 1 in which each algebra L is such that ](L) E M. Here we concentrate particularly on K1,1, its subvarieties, subdirectly irreducibles, and congruences.

(Thomas S. Blyth, J. C. Varlet)

**Book Detail :- **
** Title: ** Ockham Algebras
** Edition: **
** Author(s): ** Thomas S. Blyth, J. C. Varlet
** Publisher: ** Oxford University Press
** Series: **
** Year: ** 1994
** Pages: ** 245
** Type: ** PDF
** Language: ** English
** ISBN: ** 0198599382,9780198599388
** Country: ** UK

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**About Author :- **

The author ** Thomas S. Blyth **, University of St. Andrews. 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 **

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** • 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 **

** • Download PDF Module Theory: An Approach to Linear Algebra by Thomas S. Blyth **

** • Download PDF Ockham Algebras By Thomas. S. Blyth, J. C. Varlet **

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**Book Contents :- **
**Ockham Algebras** written by
** Thomas S. Blyth, J. C. Varlet **
cover the following topics.

0. Ordered sets, lattices, and universal algebra

1. Examples of Ockham algebras; the Berman classes

2. Congruence relations

3. Subdirectly irreducible algebras

4. Duality theory

5. The lattice of subvarieties

6. Fixed points

7. Fixed point separating congruences

8. Congruences on K1,1 -algebras

9. MS-spaces; fences, crowns

10. The dual space of a finite simple Ockham algebra

11. Relative Ockham algebras

12. Double MS-algebras

13. Subdirectly irreducible double MS-algebras

14. Congruences on double MS-algebras

15. Singles and doubles

Bibliography

Notation index

Index

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