S-Prime Graph of S-meet Semilattice

Abstract

In this paper, the S-prime ideal in a lattice \(\mathfrak{L}\) is introduced where S is the meet subset of \(\mathfrak{L}\). Also, it isshown that the prime ideal of \(\mathfrak{L}\) is an S-prime ideal of \(\mathfrak{L}\) and studied with suitable examples. Further, theS-prime ideal \(\mathfrak{I}\)\(\mathfrak{s}\) of S-meet semilattice Ls is introduced. Finally, a new graph called S-prime graph of S-meet semilattice is defined and their topological measures are generalized.