S-Prime Graph of S-meet Semilattice
Mythily C V *
Department of Mathematics, Bharathiar University PG Extension and Research centre, Erode, Tamil Nadu, India.
Kalamani D
Department of Mathematics, Bharathiar University PG Extension and Research centre, Erode, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
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 is
shown that the prime ideal of \(\mathfrak{L}\) is an S-prime ideal of \(\mathfrak{L}\) and studied with suitable examples. Further, the
S-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.
Keywords: Ideal of a lattice, lattice, partially ordered set, prime ideal, semilattice, S-prime ideal