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CHARACTERIZATIONS OF DISTRIBUTIVE LATTICES AND SEMICONTINUOUS LATTICES
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 Title & Authors
CHARACTERIZATIONS OF DISTRIBUTIVE LATTICES AND SEMICONTINUOUS LATTICES
Guanghao, Jiang; Weixue, Shi;
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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.
 Keywords
semiprime ideal;maximal ideals relative to a filter;semicontinuous lattice;semicontinuous function;semialgebraic lattice;
 Language
English
 Cited by
1.
Prime, irreducible elements and coatoms in posets, Mathematica Slovaca, 2013, 63, 6  crossref(new windwow)
2.
Strongly Semicontinuous Lattices, Electronic Notes in Theoretical Computer Science, 2017, 333, 31  crossref(new windwow)
3.
Strongly Semicontinuous Domains and Semi-FS Domains, The Scientific World Journal, 2014, 2014, 1  crossref(new windwow)
 References
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. crossref(new window)

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. crossref(new window)

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. crossref(new window)