journal-of-interdisciplinary-mathematics Journal of Interdisciplinary Mathematics 2169-012X 0972-0502 Taru Publications 10.47974/JIM-2283 Generalized homoderivations and their orthogonal properties Alhaidary Zahraa S.M. Department of Mathematics and Computer Applications, College of Applied Sciences, University of Technology, Baghdad, 10066, Iraq Faraj Anwar Khaleel Department of Mathematics and Computer Applications, College of Applied Sciences, University of Technology, Baghdad, 10066, Iraq 29 5-A 1057 1065 27 06 2026

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 (š’¦, Č”) and (āˆ‚, Āµ) of a ring š•„ are considered orthogonal if the following conditions hold for all ā„˜, Ļ„āˆˆ š•„: i. Ā  Ā If Ā š’¦ is a zero-power valued mapping and the products Ā š’¦(ā„˜)āˆ‚(Ļ„) and Č”(ā„˜)āˆ‚(Ļ„) are identical to zero. ii. Ā  Ā If the product š’¦(ā„˜)āˆ‚(Ļ„) and the compositions Č”āˆ‚ and Č”Āµ are all zero. These results offer new insights and generalizations on homoderivations in semiprime rings.

 Homoderivation Orthogonal generalized homoderivation Semiprime ring Derivation access open retracted no