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ockham algebras thomas blyth j c varlet [pdf]

Ockham Algebras By Thomas. S. Blyth, J. C. Varlet

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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
Author(s): Thomas S. Blyth, J. C. Varlet
Publisher: Oxford University Press
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.

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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
Notation index

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