Positive implicative and associative filters of lattice implication algebras
Bull. Korean Math. Soc. 1998 Vol. 35, No. 1, 53-61
Young Bae Jun, Yang Xu, and Keyun Qin
Gyeongsang National University, Southwest Jiaotong Universit, Henan Normal University
Abstract : We introduce the concepts of a positive implicative filter and an associative filter in a lattice implication algebra. We prove that (i) every positive implicative filter is an implicative filter, and (ii) every associative filter is a filter. We provide equivalent conditions for both a positive implicative filter and an associative filter.
Keywords : Lattice implication algebra, positive implicative filter, associative filter
MSC numbers : 03G10, 06B10
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