A theoretical innovation of magnified cubic translation on β−ideals

This research investigates the impact of cubic magnified translation on β-ideals, providing a theoretical exploration that incorporates µ-multiplication and (a ̅,b)-translation. By employing advanced algebraic methodologies, we analyze the homomorphic relationships induced by cubic magnified translation within the context of beta ideals. Additionally, our study explores the implications of Cartesian product results on the algebraic structures involved in this transformative process. The findings contribute to the theoretical foundations of cubic magnified translation while highlighting its potential applications in diverse mathematical contexts.