Commutativity criteria for 3-prime near-rings via zero-power valued homoderivations
DOI:
https://doi.org/10.5269/bspm.77957Abstract
In this work, we discuss the commutativity of a 3-prime near-ring N that satisfies some algebraic identities under the action of a homoderivation. Additionally, we provide examples to illustrate that the 3- primeness and zero-power valued conditions imposed in our theorems are essential and cannot be disregarded.
References
[1] E. F. Al Harfie and N. Muthana, The commutativity of prime rings with homoderivations, Int. J. Adv. Appl. Sci. 5 (5), 79-81, (2018).
[2] M. Ashraf and N. Rehman,On derivation and commutativityin prime rings, East-West J. of Mathematics 3 (1), 87-91, (2001).
[3] H. E. Bell, On derivations in near-rings II, Kluwer Academic Publishers Netherlands, 191-197, (1997).
[4] H. E. Bell and G. Mason, On derivations in near-rings, North-Holland, Math. Studies 137, 31-35, (1987).
[5] A. Boua and S. Mouhssine, Homoderivations and semigroup ideals in 3-prime near-rings, Alg. Struc. Appl. 8 (2), 177-194, (2021).
[6] A. Boua, Homoderivations and Jordan right ideals in 3-prime near-rings, AIP Conference Proceedings 2074, 020010, (2019).
[7] A. Boua and A. Raji, Several algebraic inequalities on a 3-prime near-ring, JP J. Algebr. Number T. 39 (1), 105-113, (2017).
[8] A. Boua, L. Oukhtite and A. Raji, On generalized semiderivations in 3-prime near-rings, Asian-Eur. J. Math. 9 (21), 1650036 (11 pages), (2016).
[9] A. Boua, A. Raji, A. Asma and A. Farhat, On generalized semiderivations of prime near rings, Int. J. Math. Math. Sci., 2015 (2015), 867923 (7 pages), (2015).
[10] M. M. El Sofy, Rings with some kinds of mappings, M. Sc. Thesis, Cairo University, Branch of Fayoum, (2000).
[11] A. Raji, On multiplicative derivations in 3-prime near-rings, Beitr. Algebra Geom. 65 (2), 343-357, (2024).
[12] A. Raji, Some commutativity criteria for 3-prime near-rings, Algebra Discrete Math. 32 (2), 280-292, (2021).
[13] A. Raji, On two sided α-n-derivation in 3-prime near-rings, Acta Math. Hungar. 157 (2), 465-477, (2019).
[14] A. Raji, Results on 3-prime near-rings with generalized derivations, Beitr. Algebra Geom. 57(4), 823-829, (2016).
[2] M. Ashraf and N. Rehman,On derivation and commutativityin prime rings, East-West J. of Mathematics 3 (1), 87-91, (2001).
[3] H. E. Bell, On derivations in near-rings II, Kluwer Academic Publishers Netherlands, 191-197, (1997).
[4] H. E. Bell and G. Mason, On derivations in near-rings, North-Holland, Math. Studies 137, 31-35, (1987).
[5] A. Boua and S. Mouhssine, Homoderivations and semigroup ideals in 3-prime near-rings, Alg. Struc. Appl. 8 (2), 177-194, (2021).
[6] A. Boua, Homoderivations and Jordan right ideals in 3-prime near-rings, AIP Conference Proceedings 2074, 020010, (2019).
[7] A. Boua and A. Raji, Several algebraic inequalities on a 3-prime near-ring, JP J. Algebr. Number T. 39 (1), 105-113, (2017).
[8] A. Boua, L. Oukhtite and A. Raji, On generalized semiderivations in 3-prime near-rings, Asian-Eur. J. Math. 9 (21), 1650036 (11 pages), (2016).
[9] A. Boua, A. Raji, A. Asma and A. Farhat, On generalized semiderivations of prime near rings, Int. J. Math. Math. Sci., 2015 (2015), 867923 (7 pages), (2015).
[10] M. M. El Sofy, Rings with some kinds of mappings, M. Sc. Thesis, Cairo University, Branch of Fayoum, (2000).
[11] A. Raji, On multiplicative derivations in 3-prime near-rings, Beitr. Algebra Geom. 65 (2), 343-357, (2024).
[12] A. Raji, Some commutativity criteria for 3-prime near-rings, Algebra Discrete Math. 32 (2), 280-292, (2021).
[13] A. Raji, On two sided α-n-derivation in 3-prime near-rings, Acta Math. Hungar. 157 (2), 465-477, (2019).
[14] A. Raji, Results on 3-prime near-rings with generalized derivations, Beitr. Algebra Geom. 57(4), 823-829, (2016).
Downloads
Published
2025-09-18
Issue
Section
Research Articles
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
