Nodal filters in semilattices
J C Varlet · Czech digital mathematics library · 1973
Abstracti A filter of a semilattice S is said to be nodal if it is comparable with any filter of & in the set of all filters of S ordered by inclusion.The nodal filters of 5 form a chain and induce a partition of 5 to which an interesting congruence is associated.Moreover-, the Bedekind cut of a nodal filter is again a nodal filter.Nodal filters have especially nice properties in implicative semilattices, i.e. semilattices on which a second binary operation * is defined.We characterize nodal filters solely by means of the latter operation.We also determine the sublagebras which are in direct connection with nodal filters and 9 by the way, we focus our attention on the irreducible elements of the semilattice* Finally we obtain a characterization of the nodal filters in terms of congruences.