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Volume 14 Issue 5
Oct.  2001
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Article Contents
WANG Xue-fang, XU Yang, SONG Zhen-ming. Some Properties of Filters in Lattice Implication Algebras[J]. Journal of Southwest Jiaotong University, 2001, 14(5): 536-539.
Citation: WANG Xue-fang, XU Yang, SONG Zhen-ming. Some Properties of Filters in Lattice Implication Algebras[J]. Journal of Southwest Jiaotong University, 2001, 14(5): 536-539.

Some Properties of Filters in Lattice Implication Algebras

  • Publish Date: 25 Oct 2001
  • Several equivalent conditions for filters are given, and the definition of obstinate filters is introduced. Obstinate filters, maximal implicative filters and maximal positive implicative filters are proved equivalent to each other. It is also concluded that ultrafilters are obstinate filters and obstinate filters are prime filters. An equivalent condition for the obstinate filterLis provided through implication homomorphism, that is, for arbitrary lattice implication algebraL′,there always exists an implication homomorphism fromLtoL′,such that this filter is a dual kernel of this homomorphism.

     

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