(untitled) (European Journal of Pure and Applied Mathematics, 2026)
We present the notion of n-anti-homoderivations, a novel class of additive mappings on rings. Within this framework, we establish strong necessary conditions for rings’ commutativity and the presence of nontrivial central ideals. Our approach not only generalizes several classical results as special cases, but also addresses open problems concerning the interaction between such mappings and the structural properties of rings.