Some commutativity criteria for factor rings involving three derivations

This paper focuses on factor ring [Formula: see text], where [Formula: see text] would be any arbitrary ring and [Formula: see text] is a prime ideal of [Formula: see text]. More specifically, we discuss the commutativity of [Formula: see text] by using derivations of [Formula: see text] satisfying algebraic identities involving the prime ideal [Formula: see text]. Additionally, examples are given to prove that the restrictions imposed on the hypothesis of the various theorems were necessary and not only a formality.