格蕴涵代数中滤子的若干性质
Some Properties of Filters in Lattice Implication Algebras
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摘要: 首先给出了滤子的几个等价条件,接着定义了固执滤子,证明了固执滤子,极大关联滤子,极大正关联 滤子相互等价,得出了超滤是固执滤子及固执滤子是素滤子的结论。最后通过蕴涵同态给出了格蕴涵代数L 的固执滤子的一个等价条件,即对任意一个格蕴涵代数L′,总存在一个从L到L′蕴涵同态,使这个滤子就是同 态的对偶核。Abstract: 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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Key words:
- ultrafilter /
- homomorphism /
- filter /
- lattice implication algebra
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