On Jordan ideals with left derivations in 3-prime near-rings
Main Article Content
Abstract
We will extend in this paper some results about commutativity of Jordan ideals proved in [2] and [6]. However, we will consider left derivations instead of derivations, which is enough to get good results in relation to the structure of near-rings. We will also show that the conditions imposed in the paper cannot be removed.
Downloads
Download data is not yet available.
Metrics
Metrics Loading ...
Article Details
How to Cite
En-guady, A., & Boua, A. (2023). On Jordan ideals with left derivations in 3-prime near-rings. Extracta Mathematicae, 38(1), 51-66. https://doi.org/10.17398/2605-5686.38.1.51
Issue
Section
Algebras (associative, non associative, topological)
References
[1] M. Ashraf, N. Rehman, On Lie ideals and Jordan left derivation of prime rings, Arch. Math. (Brno) 36 (2000), 201 – 206.
[2] H.E. Bell, G. Mason, On derivations in near-rings, in “Near-rings and near-fields”, North Holland Math. Stud. 137, North-Holland, Amsterdam, 1987, 31 – 35.
[3] H.E. Bell, On derivations in near-rings II, in “Nearrings, nearfields and K-loops”, Math. Appl. 426, Kluwer Acad. Publ., Dordrecht, 1997, 191 – 197.
[4] A. Boua, H.E. Bell, Jordan ideals and derivations satisfying algebraic identities, Bull. Iranian Math. Soc. 44 (2018), 1543 – 1554.
[5] A. Boua, L. Oukhtitei, A. Raji, Jordan ideals and derivations in prime near-rings, Comment. Math. Univ. Carolin. 55 (2) (2014), 131 – 139.
[6] A. Boua, Commutativity of near-rings with certain constrains on Jordan ideals, Bol. Soc. Parana. Mat. (3) 36 (4) (2018), 159 – 170.
[7] M. Brešar, J. Vukman, On left derivations and related mappings, Proc. Amer. Math. Soc. 110 (1) (1990), 7 – 16.
[8] A. Enguady, A. Boua, On Lie ideals with left derivations in 3-prime near-rings, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 68 (1) (2022), 123 – 132.
[9] S.M.A. Zaidi, M. Ashraf, A. Shakir, On Jordan ideals and left (θ, θ)-derivations in prime rings, Int. J. Math. Math. Sci. 37-40 (2004), 1957 – 1964.
[2] H.E. Bell, G. Mason, On derivations in near-rings, in “Near-rings and near-fields”, North Holland Math. Stud. 137, North-Holland, Amsterdam, 1987, 31 – 35.
[3] H.E. Bell, On derivations in near-rings II, in “Nearrings, nearfields and K-loops”, Math. Appl. 426, Kluwer Acad. Publ., Dordrecht, 1997, 191 – 197.
[4] A. Boua, H.E. Bell, Jordan ideals and derivations satisfying algebraic identities, Bull. Iranian Math. Soc. 44 (2018), 1543 – 1554.
[5] A. Boua, L. Oukhtitei, A. Raji, Jordan ideals and derivations in prime near-rings, Comment. Math. Univ. Carolin. 55 (2) (2014), 131 – 139.
[6] A. Boua, Commutativity of near-rings with certain constrains on Jordan ideals, Bol. Soc. Parana. Mat. (3) 36 (4) (2018), 159 – 170.
[7] M. Brešar, J. Vukman, On left derivations and related mappings, Proc. Amer. Math. Soc. 110 (1) (1990), 7 – 16.
[8] A. Enguady, A. Boua, On Lie ideals with left derivations in 3-prime near-rings, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 68 (1) (2022), 123 – 132.
[9] S.M.A. Zaidi, M. Ashraf, A. Shakir, On Jordan ideals and left (θ, θ)-derivations in prime rings, Int. J. Math. Math. Sci. 37-40 (2004), 1957 – 1964.