Abstract
In this paper, we introduced the concept of derivation on equality algebra \(E\) by using the notions of inner and outer derivations. Then, we investigated some properties of (inner, outer) derivation and we introduced some suitable conditions that they help us to define a derivation on \(E\). We introduced kernel and fixed point sets of derivation on \(E\) and prove that under which condition they are filters of \(E\). Finally, we prove that the equivalence relations on \((E,\rightsquigarrow ,1)\) coincide with the equivalence relations on \(E\) with derivation \( d \).
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