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Semi-Brouwerian algebras

Published online by Cambridge University Press:  09 April 2009

P. V. Ramana Murty
P. V. Ramana Murty
Affiliation:
Department of Mathematics, College of Arts, Andhra University Waltair, A.P., India
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Ever since David Ellis has shown that a Boolean algebra has a natural structure of an autometrized space, the interest in such spaces has led several authors to study various autometrized algebras like Brouwerian algebras [9], Newman algebras [4], Lattice ordered groups [6], Dually residuated lattice ordered semigroups [7] etc. However all these spaces are lattices (with the exception of Newman algebra which is not even a partially ordered set); and a natural question would be whether there are semilattices with a natural structure of an autometrized space. In the present paper we observe that the dual of an implicative semilattice [8] is a generalization of Brouwerian algebra and it has a natural structure of an autometrized space.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 3 , November 1974 , pp. 293 - 302
Copyright
Copyright © Australian Mathematical Society 1974

References

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