Bulletin of the
Korean Mathematical Society BKMS

In this paper, the concept of maximal ideals relative to a filter on posets is introduced and examined. An intrinsic characterization of distributive lattices is obtained. In addition, we also give a characterization of pseudo primes in semicontinuous lattices and a characterization of semicontinuous lattices. Functions of semicontinuous lattices which are order preserving and semicontinuous are studied. A new concept of semiarithmetic lattices is introduced and examined.

Keywords: semiprime ideal, maximal ideals relative to a filter, semicontinuous lattice, semicontinuous function, semialgebraic lattice

MSC numbers: 06A11, 06B35, 54H10