Characterizations of distributive lattices and semicontinuous lattices
Bull. Korean Math. Soc. 2010 Vol. 47, No. 3, 633-643
Published online May 1, 2010
Jiang Guanghao and Shi Weixue
Huaibei Coal Industry Teachers College and Nanjing University
Abstract : 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
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