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On the Structural Behavior of Multiplicative (Generalized)-Derivations via d-Algebra Structures

Author

Listed:
  • Hicham Saber
  • Zakia Z. Al-Amery
  • Radwan M. Al-Omary
  • Khaled Aldwoah
  • Ria Egami

Abstract

In the context of a d-algebra structure ℧,∗,0, this paper aims to introduce the concept of a multiplicative (generalized)-derivation G associated with a self-map Ξ (not necessarily a derivation). Based on this concept, the operations ∧ and composition ° will be defined, and several interesting related properties will be investigated, such as regularity, d-ideal, kernel, d-subalgebra, fixed set, and G-invariant. Moreover, we will demonstrate that by strengthening the condition of a d-algebra ℧ to include the property ℘∗℘∗ϖ=ϖ, the collection of all multiplicative (generalized)-derivations forms a semigroup on ℧. Furthermore, several relevant consequences and examples will be explored.

Suggested Citation

  • Hicham Saber & Zakia Z. Al-Amery & Radwan M. Al-Omary & Khaled Aldwoah & Ria Egami, 2026. "On the Structural Behavior of Multiplicative (Generalized)-Derivations via d-Algebra Structures," Journal of Mathematics, Hindawi, vol. 2026, pages 1-10, March.
    • Handle: RePEc:hin:jjmath:2110477
    DOI: 10.1155/jom/2110477
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