LATTICE IMPLICATIVE ALGEBRAS

In this research paper, firstly, I introduce the concept of implicative algebras and obtain certain properties. Further, I prove that implicative algebra is equipped with a structure of a bounded lattice and prove that it is lattice implication algebra. It also observes that “→” can never be associative. Secondly, we introduce two more binary operations “+” and “−“on implicative algebra and obtain certain properties with these operations. Further, we prove that any implicative algebra is a metric space. Also, we prove that every implicative algebra can be made into the regular authomethrized algebra of Swamy (1964).