BCK-algebras and BCI-algebras are abridged to two B-algebras. The BCK algebra was coined in 1966 by the Japanese mathematicians, Y. Imai and K. Iseki

Direct product plays an important role in algebraic structures. In 2019, Slamet Widianto, Sri Gemawati, Kartini

Let (M,

This shows that the direct product of two sets of GK algebra M and N is denoted by

Direct product of any two GK algebras is again a GK algebra.

Let M and N be GK algebras, let

We know that

Since

This implies that

Now let us prove it is GK algebra.

Let

Hence

Let

If

Let

Let

We have to prove

If

=

This implies that

We have to prove

Let

Now, to prove

Hence

Let

Ker

Let us consider the mapping

If the map

for

Therefore

Let

Hence Ker

In this article we discussed about the concept of the direct product of GK algebra. We derived the finite form of direct product of GK algebra is isomorphism and also, we investigated and applied the concept of direct product of GK algebra in GK homomorphism and GK kernel, then obtained interesting results.