Extensions of the Glivenko‐type congruences on a Stone lattice
Abd El‐Mohsen Badawy · Mathematical Methods in the Applied Sciences · 2017
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 2 extensions of the Glivenko‐type congruences are permutable.