대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제47권3호
  • /
  • Pages.633-643
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  • 2010
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2009.01.10
  • 발행 : 2010.05.31
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초록

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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참고문헌

  1. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott, A Compendium of Continuous Lattices, Springer-Verlag, Berlin-New York, 1980.
  2. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott, Continuous Lattices and Domains, Cambridge University Press, Cambridge, 2003.
  3. K. H. Hofmann and J. D. Lawson, Irreducibility and generation in continuous lattices, Semigroup Forum 13 (1976/77), no. 4, 307-353. https://doi.org/10.1007/BF02194952
  4. G. H. Jiang and G. P. Wang, Locally maximal ideals on posets, J. Xuzhou Norm. Univ. Nat. Sci. Ed. 24 (2006), no. 1, 11-14.
  5. Y. Ray, Semiprime ideals in general lattices, J. Pure Appl. Algebra 56 (1989), no. 2, 105-118. https://doi.org/10.1016/0022-4049(89)90140-0
  6. X. H. Wu, Q. G. Li, and R. F. Xu, Some properties of semicontinuous lattices, Mohu Xitong yu Shuxue 20 (2006), no. 4, 42-46.
  7. D. Zhao, Semicontinuous lattices, Algebra Universalis 37 (1997), no. 4, 458-476. https://doi.org/10.1007/s000120050031

피인용 문헌

  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