Generalized homoderivations and their orthogonal properties

Alhaidary, Zahraa S.M.; Faraj, Anwar Khaleel

doi:10.47974/JIM-2283

Open Access Research Article

Generalized homoderivations and their orthogonal properties

^*Zahraa S.M. AlhaidaryCorresponding authorzahraa.s.mohammed@uotechnology.edu.iqDepartment of Mathematics and Computer Applications College of Applied Sciences University of Technology Department of Applied Sciences Branch of Mathematics and Computer Applications University of Technology Baghdad, 10066, Iraq0009-0008-2248-3644View full profile → , Anwar Khaleel FarajAnwar.K.Faraj@uotechnology.edu.iqDepartment of Mathematics and Computer Applications College of Applied Sciences University of Technology Baghdad, 10066, IraqView full profile →

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pp. 1057–1065Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2283XML

Received:: 01 May 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2283
Pages:: 1057–1065

Abstract

This paper investigates the orthogonality of generalized homoderivation mappings in semiprime rings, with an emphasis on specific identities involving their product and composition. The concept of orthogonal generalized homoderivations is introduced, broadening the scope of previously established results. Two Generalized homoderivation mappings (𝒦, ȡ) and (∂, µ) of a ring 𝕄 are considered orthogonal if the following conditions hold for all ℘, τ∈ 𝕄: i. If 𝒦 is a zero-power valued mapping and the products 𝒦(℘)∂(τ) and ȡ(℘)∂(τ) are identical to zero. ii. If the product 𝒦(℘)∂(τ) and the compositions ȡ∂ and ȡµ are all zero. These results offer new insights and generalizations on homoderivations in semiprime rings.

Keywords

Homoderivation Orthogonal generalized homoderivation Semiprime ring Derivation

Subject Classifications

16N6016W25

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