A Characterization of Frobenius Derivations and Automorphisms of a Class of Local Near-Rings

Abstract

In this chapter, we use the idealization procedure for finite rings to construct a class of local quasi-3 prime Near-Rings N with a Jordan ideal J(N ) and admitting a Frobenius derivation. The structural characterization of N ; J(N ) and commutation of N via the Frobenius derivations have been explicitly determined. This work has also been extended to an investigation of the symmetries of the graphs ?(N ) of the classes of near-rings N studied. Indeed some structures and orders of the automorphism groups of ?(N ) have been determined.