Structure and Applications of $(p, q)$-Derivations in Algebra
Functional Analysis
2025-09-05 v1
Abstract
In this paper, we investigate -derivations in both general algebras and Banach algebras. Our main result extends the Singer-Wermer theorem to -derivations, proving that their ranges are contained in the radical of the algebra. As a direct consequence, we prove that the range of any left derivation lies within the radical of the algebra even without assuming continuity. This improves a result due to Bra\v{s}er and Vukman. For Banach algebras, we show that primitive ideals remain invariant under bounded -derivations. Finally, we study -derivations of group algebras and give an answer to the question posed.
Cite
@article{arxiv.2509.04103,
title = {Structure and Applications of $(p, q)$-Derivations in Algebra},
author = {Mohammad Javad Mehdipour and Narjes Salkhordeh},
journal= {arXiv preprint arXiv:2509.04103},
year = {2025}
}