- Volume 47 Issue 3
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.
semiprime ideal;maximal ideals relative to a filter;semicontinuous lattice;semicontinuous function;semialgebraic lattice
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