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.

arXiv commentThe results in this paper are added to my other paper, ''Generalized Homogeneous Derivations on Graded Rings'' [arXiv:2412.17187] as Section. So this paper is no longer of interest, and the results we have proved here are being moved to my other paper