ON QUASI-LATTICE IMPLICATION ALGEBRAS
Yong Ho Yon · Journal of applied mathematics & informatics · 2015
The notion of quasi-lattice implication algebras is a generalization of lattice implication algebras. In this paper, we give an optimized definition of quasi-lattice implication algebra and show that this algebra is a distributive lattice and that this algebra is a lattice implication algebra. Also, we define a congruence relation ΦF induced by a filter F and show that every congruence relation on a quasi-lattice implication algebra is a congruence relation ΦF induced by a filter F.