Some commutativity criteria of a factor ring R/P using semiderivations of R

Let [Formula: see text] be a ring and [Formula: see text] a prime ideal of [Formula: see text] This paper establishes a connection between the commutativity of the factor ring [Formula: see text] and semiderivations of [Formula: see text] satisfying some algebraic identities involving the prime ideal [Formula: see text] Moreover, we extended some results for derivations and semiderivations of prime rings to semiprime rings.