Generalized Homogeneous Derivations on Graded Rings
Rings and Algebras
2026-03-24 v6
Abstract
We introduce a notion of generalized homogeneous derivations on graded rings as a natural extension of the homogeneous derivations defined by Kanunnikov. We then define gr-generalized derivations, which preserve the degrees of homogeneous components. Several significant results originally established for prime rings are extended to the setting of gr-prime rings, and we characterize conditions under which gr-semiprime rings contain nontrivial central graded ideals. In addition, we investigate the algebraic and module-theoretic structures of these maps, establish their functorial properties, and develop categorical frameworks that describe their derivation structures in both ring and module contexts.
Cite
@article{arxiv.2412.17187,
title = {Generalized Homogeneous Derivations on Graded Rings},
author = {Yassine Ait Mohamed},
journal= {arXiv preprint arXiv:2412.17187},
year = {2026}
}