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Coproducts of De Morgan algebras

Published online by Cambridge University Press:  17 April 2009

William H. Cornish  and
Peter R. Fowler
William H. Cornish
Affiliation:
School of Mathematical Sciences, Flinders University of South Australia, Bedford Park, South Australia.
Peter R. Fowler
Affiliation:
School of Mathematical Sciences, Flinders University of South Australia, Bedford Park, South Australia.
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Abstract

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The dual of the category of De Morgan algebras is described in terms of compact totally ordered-disconnected ordered topological spaces which possess an involutorial homeomorphism that is also a dual order-isomorphism. This description is used to study the coproduct of an arbitrary collection of De Morgan algebras and also to represent the coproduct of two De Morgan algebras in terms of the continuous order-preserving functions from the Priestley space of one algebra to the other algebra, endowed with the discrete topology. In addition, it is proved that the coproduct of a family of Kleene algebras in the category of De Morgan algebras is the same as the coproduct in the subcategory of Kleene algebras if and only if at most one of the algebras is not boolean.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 1 , February 1977 , pp. 1 - 13
Copyright
Copyright © Australian Mathematical Society 1977

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