- Volume 47 Issue 3
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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
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.
semiprime ideal;maximal ideals relative to a filter;semicontinuous lattice;semicontinuous function;semialgebraic lattice
- 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.
- 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.
- 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
- 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.
- 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
- 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.
- D. Zhao, Semicontinuous lattices, Algebra Universalis 37 (1997), no. 4, 458-476. https://doi.org/10.1007/s000120050031
- Prime, irreducible elements and coatoms in posets vol.63, pp.6, 2013, https://doi.org/10.2478/s12175-013-0163-9
- Strongly Semicontinuous Lattices vol.333, 2017, https://doi.org/10.1016/j.entcs.2017.08.004
- Strongly Semicontinuous Domains and Semi-FS Domains vol.2014, 2014, https://doi.org/10.1155/2014/262648