Certain functional identities involving a pair of homogeneous derivations with central values in gr-prime rings

Abstract

In this paper, we explore functional identities with central values in gr-prime rings involving pairs of homogeneous derivations. We establish commutativity conditions that extend classical results from prime rings to the graded setting. In particular, we show that under certain conditions on homogeneous derivations, the ring must be commutative. Furthermore, we demonstrate that these results cannot be extended to gr-semiprime rings.