A STUDY OF DERIVATIONS AND LINEAR MAPPINGS ON SKEW GENERALIZED POWER SERIES MODULES

This paper investigates the structure of skew generalized power series modules over skew generalized power series rings, emphasizing the extension of derivations in this context. We define and study additive mappings that generalize classical derivations with respect to module homomorphisms and ring derivations. Under suitable compatibility conditions, we construct corresponding derivations on skew generalized power series modules and establish their fundamental properties. These findings contribute to a broader understanding of how derivations can be systematically extended from classical module theory to generalized algebraic frameworks.