Abstract
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 Φ<sub>F</sub> induced by a filter F and show that every congruence relation on a quasi-lattice implication algebra is a congruence relation Φ<sub>F</sub> induced by a filter F.
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