Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CHARACTERIZATIONS OF DISTRIBUTIVE LATTICES AND SEMICONTINUOUS LATTICES

  • Guanghao, Jiang (Department of Mathematics Huaibei Coal Industry Teachers College) ;
  • Weixue, Shi (Department of Mathematics Nanjing University)
  • Received : 2009.01.10
  • Published : 2010.05.31
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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.

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References

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Cited by

  1. Prime, irreducible elements and coatoms in posets vol.63, pp.6, 2013, https://doi.org/10.2478/s12175-013-0163-9
  2. Strongly Semicontinuous Lattices vol.333, 2017, https://doi.org/10.1016/j.entcs.2017.08.004
  3. Strongly Semicontinuous Domains and Semi-FS Domains vol.2014, 2014, https://doi.org/10.1155/2014/262648