A characterization of weak $$n_m$$ n m -Jordan $$(\alpha ,\beta )$$ ( α , β ) -derivations by generalized centralizers

Abstract

The main purpose of this paper is to prove the following result: Let \(D:\mathcal {R} \rightarrow \mathcal {R}\) be a weak \(n_m\)-\(Jordan\) (\(\alpha ,\beta )\)-derivation. Suppose that \(\mathcal {R}\) is a unital \(2^{p - 2}p!\)-torsion free semiprime ring such that \(mn(n - 1) \ | \ p!\). Then, under certain condition, \(D\) is an (\(\alpha ,\beta \))-derivation.