Online Resource
Cambridge University Press (CUP)
;
1974
In:
Journal of the Australian Mathematical Society Vol. 18, No. 3 ( 1974-11), p. 293-302
In:
Journal of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 18, No. 3 ( 1974-11), p. 293-302
Abstract:
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 of Medium:
Online Resource
ISSN:
0004-9735
DOI:
10.1017/S1446788700022874
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1974
detail.hit.zdb_id:
1478743-X
SSG:
17,1
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