On Centrally Extended Generalized Jordan ∗-derivations and Related Maps in Rings Hafedh Alnoghashi, Rwaida A. Bahah, Maimona S. Zghyu Maps Preserving Products and Derivations Advances in Algebraic Structures, 2026 Let R be a 2-torsion-free noncommutative prime ring with involution * with center, Z. In this article, we introduce the notion of a centrally extended generalized Jordan *-derivation. We show that if R admits a centrally extended generalized Jordan *-derivation Γ associated with a centrally extended Jordan *-derivation θ, and satisfies the condition [Γ(a),a] ∈ Z (resp., [Γ(a),a*] ∈ Z) for all a ∈ R, then either Γ(a) = λ a and θ(a) = λ (a−a*) (resp., Γ(a) = λ a*) for all a ∈ R, where λ belongs to the extended centroid of R, or R satisfies the standard identity S4. Furthermore, we present examples to highlight the significance of the conditions imposed in our findings.
Left Ideals Satisfying Central-Valued Identities Modulo Semiprime Ideals via Multiplicative (Generalized) Derivations Amal S. Alali, Abdelkarim Boua, Claus Haetinger, Nadeem ur Rehman, Hafedh Alnoghashi Journal of Mathematics, 2026 In this study, we investigate the behavior of semiprime ideals that satisfy certain algebraic identities using multiplicative (generalized) derivations. In addition, examples are provided to show that the limits imposed on the hypotheses of the different theorems are not superfluous.
Additivity and Central Behavior of CE-Generalized Homoderivations in Associative Rings Hicham Saber, Hafedh Alnoghashi, Radwan M. Al-Omary, Khaled Aldwoah, Bakri Younis, M. I. Elashiry Journal of Mathematics, 2026 This study examines the commutativity of a ring endowed with a special class of mappings termed centrally extended generalized homoderivations. These mappings serve as an extension of several existing concepts, including homoderivations, generalized homoderivations, and left centralizers. The paper further explores distinctive structural characteristics of the center associated with such rings, emphasizing how these mappings influence their algebraic behavior and internal consistency.
On the Structure of Quotient Rings R/P via Identities with Multiplicative (Generalized) Derivations Ali Yahya Hummdi, Hafedh Alnoghashi, Radwan M. Al-omary, Rwaida A. Bahah Mathematics, 2025 This work investigates the structure of an arbitrary ring R that contains a two-sided ideal I and a prime ideal P satisfying the condition P⊊I. Our analysis centers on the consequences of several identities that involve three multiplicative (generalized) derivations, denoted by Θ1, Θ2, Θ3:R→R. These are associated with maps θ1, θ2, θ3:R→R, which are not presumed to be additive or to be derivations themselves. The study further incorporates a non-zero derivation Δ along with two arbitrary, potentially non-additive, maps Γ1, Γ2:R→R. We establish conditions under which these identities lead to significant structural properties of the ring. To underscore the importance of our assumptions, we construct an example demonstrating that the primeness hypothesis on the ideal P is indispensable for our main conclusions.
On b-generalized derivations and commutativity of prime rings Hafedh M. Alnoghashi, Junaid Nisar, Nadeem ur Rehman, Radwan M. Al-Omary Revista Colombiana De Matematicas, 2025 Let A be a prime ring, Z(A) its center, Q its right Martindale quotient ring, C its extended centroid, ψ a non-zero b-generalized derivation of A with associated map ξ. In this article, we prove that: (i) If [ψ(x), ψ(y)] = 0 for all x, y ∈ A, then A is either commutative or there exists q ∈ Q such that ξ = ad(q), ψ(x) = -bxq, and qb = 0. (ii) If ψ(x) ◦ ψ(y) = 0 for all x, y ∈ A, then A is either commutative with char(A) = 2 or there exists q ∈ Q such that ψ(x) = -bxq and qb = 0. Additional results are established for cases involving [ξ(x), ψ(x)] = 0 or ξ(x)◦ψ(x) = 0, where char(A) = 2. Furthermore, we give some examples that show the importance of the hypotheses of our theorems.
On Ideals and Behavior of Quotient Rings via Generalized (α,β)-Derivations Nawaf L. Alsowait, Mohammed Al-Shomrani, Radwan M. Al-omary, Zakia Z. Al-Amery, Hafedh Alnoghashi Mathematics, 2025 The purpose of this paper is to examine the behavior of a factor ring R/P with a partial range I of a ring R, where P is a prime ideal of R and I is a non-zero ideal of R such that P⊊I. In order to accomplish this objective, we will utilize specific algebraic identities that involve P and are related to generalized (α,β)-derivations F and G, associated with (α,β)-derivations d and g, respectively, where α and β are automorphisms of R. Additionally, we will list some important related consequences. Finally, we will provide an illustrative example to emphasize the importance of the hypotheses imposed in our theorems.
Left Ideals Satisfying Central‐Valued Identities Modulo Semiprime Ideals via Multiplicative (Generalized) Derivations AS Alali, A Boua, C Haetinger, N Rehman, H Alnoghashi Journal of Mathematics 2026 (1), 9920403 , 2026 2026
Additivity and Central Behavior of CE‐Generalized Homoderivations in Associative Rings H Saber, H Alnoghashi, RM Al-Omary, K Aldwoah, B Younis, MI Elashiry Journal of Mathematics 2026 (1), 5814570 , 2026 2026
On Centrally Extended Generalized Jordan*-derivations and Related Maps in Rings H Alnoghashi, RA Bahah, MS Zghyu Maps Preserving Products and Derivations, 170-189 , 2026 2026
On the Structure of Generalized Semiderivations in Prime Rings H Alnoghashi, N Rehman Algebra and Differential Equations with Applications 508, 125-130 , 2026 2026
On the Structure of Quotient Rings R / P via Identities with Multiplicative (Generalized) Derivations AY Hummdi, H Alnoghashi, RM Al-omary, RA Bahah Mathematics 13 (19), 3208 , 2025 2025
Endomorphisms on prime rings with antiautomorphisms: H. Alnoghashi et al. H Alnoghashi, C Abdioğlu, MA Raza, N ur Rehman Ricerche di Matematica 74 (4), 2283-2296 , 2025 2025
On Ideals and Behavior of Quotient Rings via Generalized ( α , β )-Derivations NL Alsowait, M Al-Shomrani, RM Al-omary, ZZ Al-Amery, H Alnoghashi Mathematics 13 (6), 968 , 2025 2025 Citations: 2
Semiderivations in Prime Rings H Alnoghashi, N Rehman Algebra and Differential Equations with Applications: SICMA-2023, Antalya … , 2025 2025
A Pair of Generalized (α, α)‐Derivations With Identities Related to Prime Ideals AY Hummdi, H Alnoghashi, RM Al-Omary, A Boua Journal of Mathematics 2025 (1), 2291842 , 2025 2025 Citations: 1
A Note on Skew Derivations and Antiautomorphisms of Prime Rings FA Alqarni, NUR Rehman, H Alnoghashi, J Nisar, O Al-Mallah Journal of Mathematics 2025 (1), 5589151 , 2025 2025
Characterizing multiplicative (generalized)-derivations on semiprime rings satisfying specific functional identities IU Huque, H Alnoghashi Rendiconti del Circolo Matematico di Palermo Series 2 74 (33), 1-9 , 2025 2025
Commutativity of prime rings involving multiplicative b-generalized derivation W Ahmed, MR Mozumder, A Abbasi, H Alnoghashi Journal of Algebra and Related Topics 13 (2), 165-176 , 2025 2025
Commutativity and Prime Ideals in Rings with Involutions via Derivations RM Al-omary, H ALNOGHASHI, J Nisar, N Rehman Journal of Mathematical Extension 18 , 2024 2024
Nonlinear Mixed -Jordan Triple Derivation on -algebras AS Alali, N Rehman, HM Alnoghashi European Journal of Pure and Applied Mathematics 17 (4), 3399-3414 , 2024 2024
On b-generalized derivations and commutativity of prime rings. HM Alnoghashi, J Nisar, N ur Rehman, RM Al-Omary Revista Colombiana de Matemáticas 58 (2) , 2024 2024
T-Commuting Generalized Derivations on Ideals and Semi-Prime Ideal N Rehman, HM Alnoghashi Boletim da Sociedade Paranaense de Matematica 42, 1-15 , 2024 2024 Citations: 1
Results on Generalized Derivations in Prime Rings with Involution FA Alqarni, N ur Rehman, HM Alnoghashi Advances in Ring Theory and Applications 443, 363-373 , 2024 2024
Prime Rings with Involution FA Alqarni, N ur Rehman, HM Alnoghashi Advances in Ring Theory and Applications: WARA22, Messina, Italy, July 18–20 … , 2024 2024
On skew derivations and antiautomorphisms in prime rings AS Alali, H Alnoghashi, J Nisar, N ur Rehman, FA Alqarni Georgian Mathematical Journal 31 (2), 173-179 , 2024 2024 Citations: 3
The first nonlinear mixed Jordan triple derivation on*-algebras N ur Rehman, J Nisar, HM Alnoghashi Filomat 38 (8), 2773-2783 , 2024 2024 Citations: 5
MOST CITED SCHOLAR PUBLICATIONS
Action of prime ideals on generalized derivations-I HM Alnoghashi arXiv preprint arXiv:2107.06769 , 2021 2021.0 Citations: 21
Identities in a prime ideal of a ring involving generalized derivations N ur Rehman, HMAAA Boua Kyungpook mathematical journal 61 (4), 727-735 , 2021 2021.0 Citations: 19
On generalized derivations involving prime ideals N Rehman, M Hongan, HM Alnoghashi Rendiconti del Circolo Matematico di Palermo Series 2 71 (2), 601-609 , 2022 2022.0 Citations: 18
Commutativity of prime rings with generalized derivations and anti-automorphisms NU Rehman, HM Alnoghashi Georgian Mathematical Journal 29 (4), 583-594 , 2022 2022.0 Citations: 16
A generalization of Posner’s theorem on generalized derivations in rings N Rehman, EK Sogutcu, HM Alnoghashi Journal of the Iranian Mathematical Society 3 (1), 1-9 , 2022 2022.0 Citations: 15
-Commuting Generalized Derivations on Ideals and Semi-Prime Ideal-II NU Rehman, HM Alnoghashi Matematychni Studii 57 (1), 98-110 , 2022 2022.0 Citations: 13
A note on generalized derivations on prime ideals N Rehman, HM Alnoghashi, M Hongan Journal of Algebra and Related Topics 10 (1), 159-169 , 2022 2022.0 Citations: 12
On Multiplicative (Generalized)‐Derivation Involving Semiprime Ideals HM Alnoghashi, S Naji, NU Rehman Journal of Mathematics 2023 (1), 8855850 , 2023 2023.0 Citations: 10
Action of prime ideals on generalized derivations-I. arXiv 2021 N Rehman, H Al Noghashi arXiv preprint arXiv:2107.06769 , 0 Citations: 10
On generalized derivations involving prime ideals with involution N Rehman, HM Alnoghashi, M Hongan Ukrainian Mathematical Journal 75 (8), 1219-1241 , 2024 2024.0 Citations: 9
Action of prime ideals on generalized derivations-I. arXiv N Rehman, H Al Noghashi arXiv preprint arXiv:2107.06769 , 2021 2021.0 Citations: 7
The first nonlinear mixed Jordan triple derivation on*-algebras N ur Rehman, J Nisar, HM Alnoghashi Filomat 38 (8), 2773-2783 , 2024 2024.0 Citations: 5
Results on generalized derivations in prime rings HM Alnoghashi, FA Al-Qarni, NU Rehman Algebraic Structures and Their Applications 10 (2), 87-98 , 2023 2023.0 Citations: 5
Centrally extended Jordan (∗)-derivations centralizing symmetric or skew elements AS Alali, HM Alnoghashi, N Rehman Axioms 12 (1), 86 , 2023 2023.0 Citations: 5
Differential identities on ideals in prime rings M Hongan, N ur Rehman, HM Alnoghashi Afrika Matematika 33 (3), 78 , 2022 2022.0 Citations: 5
Jordan homo-derivations on triangular matrix rings NU Rehman Annals of the Alexandru Ioan Cuza University-Mathematics , 2022 2022.0 Citations: 5
Some classification theorems and endomorphisms in new classes H Alnoghashi, AS Alali, EK Sogutcu, N Rehman, FA Alqarni Mathematics 11 (18), 3910 , 2023 2023.0 Citations: 4
A pair of derivations on prime rings with antiautomorphism FA Alqarni, AS Alali, H Alnoghashi, NU Rehman, C Haetinger Mathematics 11 (15), 3337 , 2023 2023.0 Citations: 4
On skew derivations and antiautomorphisms in prime rings AS Alali, H Alnoghashi, J Nisar, N ur Rehman, FA Alqarni Georgian Mathematical Journal 31 (2), 173-179 , 2024 2024.0 Citations: 3
On Ideals and Behavior of Quotient Rings via Generalized ( α , β )-Derivations NL Alsowait, M Al-Shomrani, RM Al-omary, ZZ Al-Amery, H Alnoghashi Mathematics 13 (6), 968 , 2025 2025.0 Citations: 2