The commutative residuated lattices were first introduced by M. Ward and R.P. Dilworth as
generalization of ideal lattices of rings. Complete studies on residuated lattices were developed by H.
Ono, T. Kowalski, P. Jipsen and C. Tsinakis. Also, the concept of lattice implication algebra is due to Y.
Xu. And Luitzen Brouwer founded the mathematical philosophy of intuitionism, which believed that a
statement could only be demonstrated by direct proof. Arend Heyting, a student of Brouwer’s, formalized
this thinking into his namesake algebras. In this paper, we investigate the relationship between implicative
algebras, Heyting algebras and residuated lattices. In fact, we show that implicative algebras and Heyting
algebras can be described as residuated lattices.