What is it about?
In this paper the notions of annulets and normal filters are introduced in Stone lattices and their properties are studied. A set of equivalent conditions is obtained to characterize normal filters of a Stone lattice. The extensions of the Glivenko type congruences on a Stone lattice are investigated via annulets and normal filters. A description of the lattice of all extensions of the Glivenko type congruences on a Stone lattice is given. A one-to-one correspondence between the class of all extensions and the class of all normal filters of a Stone lattice is obtained. Finally, we observe that every two extensions of the Glivenko type congruences are permutable.
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Why is it important?
The studying of congruence relation related to congruence relations is very important for the class of Stone lattices and for lattices in genral.
Perspectives
I think that this article is useful for development areas of Stone algebras and MS-algebras.
Abd El-Mohsen Badawy
Mathematics Depatement Faculty of Science Tanta University Egypt
Read the Original
This page is a summary of: Extensions of the Glivenko-type congruences on a Stone lattice, Mathematical Methods in the Applied Sciences, July 2017, Wiley,
DOI: 10.1002/mma.4492.
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