Revista de la
Unión Matemática Argentina
On graded rings with homogeneous derivations
Yassine Ait Mohamed

Volume 69, no. 1 (2026), pp. 55–69    

Published online (final version): November 21, 2025

https://doi.org/10.33044/revuma.4934

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Abstract

We establish results related to homogeneous derivations, a concept introduced by Kanunnikov (2018). First, we prove the existence of a non-trivial family of derivations that are not homogeneous on graded rings. Furthermore, based on homogeneous derivations, we extend certain existing significant results in the context of prime (resp. semiprime) rings to gr-prime (resp. gr-semiprime) rings, such as Posner's and Herstein's theorems.

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