Some Equations in Rings Involving Semiprime Ideals and Multiplicative Generalized Semiderivations

This paper examines the commutativity of the quotient ring F/Y by utilizing specific differential identities in a general ring F that contains a semiprime ideal Y. This study particularly focuses on the role of a multiplicative generalized semiderivation ψ, which is associated with a map θ, in determining the commutative nature of the quotient ring.