Structure and Applications of $(p, q)$-Derivations in Algebra

Mohammad Javad Mehdipour; Narjes Salkhordeh

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arXiv · 2509.04103

Structure and Applications of $(p, q)$-Derivations in Algebra

Mohammad Javad Mehdipour·Narjes Salkhordeh

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Abstract

In this paper, we investigate $(p, q)$-derivations in both general algebras and Banach algebras. Our main result extends the Singer-Wermer theorem to $(p, q)$-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 Brašer and Vukman. For Banach algebras, we show that primitive ideals remain invariant under bounded $(p, q)$-derivations. Finally, we study $(p, q)$-derivations of group algebras and give an answer to the question posed.

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BibTeX RIS

Mohammad Javad Mehdipour, Narjes Salkhordeh. 2025-09-04. Structure and Applications of $(p, q)$-Derivations in Algebra. https://arxiv.org/abs/2509.04103

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