Generalized Left Derivations with Identities on Near-Rings
Keywords:Derivations, Generalized left derivations, Left derivations, 3-Prime near-ring s, Semigroup ideals
In this paper, new concepts which are called: left derivations and generalized left derivations in nearrings have been defined. Furthermore, the commutativity of the 3-prime near-ring which involves some
algebraic identities on generalized left derivation has been studied.
Published Online First 20/3/2023
Pilz G. North Holland Mathematics Studies. 2nd edition. Amsterdam: American Elsevier; 1983. Chap. 32, Near-rings: The Theory and its Applications; p. 1-470.
Wang X. Derivations in prime near-rings. Proc. Am Math Soc. 1994; 121: 361–366.
Boua A. Some Identities in Rings and Near-Rings with Derivations. J Math. 2021; 45(1): 75-80.
Ali A, Boua A, Farhat A. Semigroup ideals and generalized semiderivations of prime near rings. Bol Soc Paran Mat. 2019; 37(4): 25-45.
Ashraf M, Boua A, Aslam M. generalized multiplicative derivations in 3-prime near rings. Math Slovaca. 2019; 68(2): 331-338
Boua A, Farhan E. Generalized derivations on near-rings with identities. J Discret Math Sci. Cryptogr. 2021; 26(4): 1-14.
En-guady A, Boua A, Farhan E. Some Identities of 3-Prime Near-Rings Involving Jordan Ideals and Left Generalized Derivations. Iraqi J Sci. 2021; 62(6): 1961-1967.
Boua A. Structure of 3-prime near-rings satisfying some identities. Commun. Korean Math Soc. 2019; 34(1): 17-26
Farhan E. A Study on n-Derivation in Prime Near – Rings. Iraqi J Sci. 2020; 61(3): 620-624.
Farhan E. α-N-derivations in prime near – rings. AIP Conf Proc. 2019; 2201(1): 020011.
Farhan E. Generalized n-Derivation in Prime Near – Rings. Sci Int (Lahore). 2018; 30(6): 865-868.
Boua A. Homoderivations and Jordan right ideals in 3-prime near-rings. AIP Conf Proc. 2019; 2074(1): 020010. https: // doi.org / 10.1063/ 1.5090627 .
Mouhssine S, Boua A. Homoderivations and Semigroup Ideala in 3-Prime Near-Rings.. Alg Struc Appl. 2021; 8(2): 177-194.
Boua A and Farhan E. Generalized homoderivations in near-rings. Indian J Math. 2021; 63(2): 229-242.
Majeed A, Farhan E. Right n-derivations in prime near–rings. Qadisiyah j Pure sci. 2016; 21(3): 31-41. https://qpures.iraqjournals.com/article_122390_4bdcccfdbd181121c2f6b9dbfce3a0d1.pdf
Farhan E. Near – Rings with Generalized Right n-Derivations. Iraqi J Sci. 2021; 62(7): 2334-2342.
Brešar M, Vukman J. On left derivations and related mappings. Proc Am Math. 1999; 110: 7–16.
Mahmood AH. Notes on Traces of a Symmetric Generalized (σ, τ)-Biderivations and Commutativity in Prime Rings, Baghdad Sci J. 2017; 14(1): 213-218.
Saed IA. Jordan left (θ-θ) -derivations Of σ -prime rings. Baghdad Sci J. 2011; 8(3): 826-831
Copyright (c) 2023 Baghdad Science Journal
This work is licensed under a Creative Commons Attribution 4.0 International License.