Structure of a factor ring $R\mathrm{/}P$ in terms of differential identities involving a new kind of involution

Let $R$ be a ring and $P$ a prime ideal of $R\mathrm{.}$ In this paper, we establish some commutativity criteria for the factor ring $R\mathrm{/}P$ in terms of derivations of $R$ satisfying some algebraic identities involving a new kind of involution in relation with $P\mathrm{.}$