M− Prime Ideals in Lattices and Their M− Prime Spectrum

Abstract

In this paper, we explore various characteristics and attributes of prime ideals, minimal prime ideals, and weakly prime ideals in a lattice. We demonstrate that the image and inverse image of an prime ideal (or weakly prime ideal) also qualify as an prime ideal (or weakly prime ideal). Additionally, we investigate the relationship between prime ideals and weakly prime ideals. Finally, we introduce the concept of the space of prime ideals and discuss their characterizations.