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


How to Cite

C V, Mythily, and Kalamani D. 2024. “S-Prime Graph of S-Meet Semilattice”. Asian Research Journal of Mathematics 20 (10):15-29. https://doi.org/10.9734/arjom/2024/v20i10841.