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http://dx.doi.org/10.4134/BKMS.2010.47.3.633

CHARACTERIZATIONS OF DISTRIBUTIVE LATTICES AND SEMICONTINUOUS LATTICES  

Guanghao, Jiang (Department of Mathematics Huaibei Coal Industry Teachers College)
Weixue, Shi (Department of Mathematics Nanjing University)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.3, 2010 , pp. 633-643 More about this Journal
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;
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