On n-Jordan homoderivations in rings

Abstract

Abstract Let R be a ring and let n ≥ 1 {n\geq 1} be a fixed integer. An additive mapping h of a ring R into itself is called an n-Jordan homoderivation if h ⁢ ( x n ) = ( h ⁢ ( x ) + x ) n - x n {h(x^{n})=(h(x)+x)^{n}-x^{n}} holds for all x ∈ R {x\in R} . In this paper, we initiate the study of n-Jordan homoderivations on rings. Precisely, we characterize n-Jordan homoderivations in terms of homoderivations and anti-homomorphisms under certain conditions. Finally, we conclude our paper with a direction for further research.