Published Paper Details:

Near-rings constitute a significant generalization of rings and semigroups, offering a flexible algebraic framework for both theoretical exploration and applied contexts. A left near - ring N is called weak commutative if xyz = xzy for every x,y,z ? N. A left near - ring N is called pseudo commutative if xyz = zyx for every x,y,z ? N. A left near - ring N is called quasi weak commutative near- ring if xyz = yxz for every x,y,z ? N. We establish fundamental results concerning the existence, uniqueness, and characterization of ideals within these classes and provide necessary and sufficient conditions under which a left Boolean near-ring admits a quasi-weak commutative structure.This findings not only extend existing results in near-ring theory but also highlight potential avenues for applications in automata theory, cryptographic systems, and error-correcting codes. These results enrich the structural understanding of near-rings, provide new tools for analysing their ideal theory, and suggest applications in coding theory and cryptography where idempotent-based algebraic systems are of particular interest.