Fractal structure of nearrings based on permutation identities

For (Formula presented.) and for a permutation σ on k letters, the identity of the form (Formula presented.) is called a permutation identity. Fractals are self-similar structures exhibiting self-similarity at all scales. Algebraic structures that exhibit fractal-like nature are of great interest. Using the notion of permutation identities, we obtain self-similar infinite substructures of a nearring. We extend the notion of ideal of a nearring by defining product fractal ideal of a nearring. We obtain the quotient structure induced by fractal ideals and derive fractal isomorphism theorems for nearrings.