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

Authors

  • Mohammad Javad Mehdipour
  • Narjes Salkhordeh

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 Bra\v{s}er 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.

Published

2025-12-29

Issue

Vol. 20

Section

Vol. 20, No. 2, (2026)

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