Abstract As we know several algebras with one binary, one unary and two nullary operations introduced as an algebraic logic structure. One of them is implicative algebra which is equipped in other branches of sciences like computational intelligence, lattice theory, fuzzy theory, etc. In this paper, firstly, we introduce the concept of implicative algebras and obtain certain properties. Further we prove that implicative algebra is equipped with a structure of a bounded lattice and prove that it is a 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 a regular authometrized algebra of swamy (1964).