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arXiv · 2412.17187

Generalized Homogeneous Derivations on Graded Rings

Yassine Ait Mohamed
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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.

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Yassine Ait Mohamed. 2024-12-22. Generalized Homogeneous Derivations on Graded Rings. https://arxiv.org/abs/2412.17187

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