CHARACTERIZATIONS OF DISTRIBUTIVE LATTICES AND SEMICONTINUOUS LATTICES
Jiang Guanghao, Shi Weixue · Bulletin of the Korean Mathematical Society · 2010
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.