On Jordan ideals with left derivations in 3-prime near-rings

Authors

  • A. En-guady Department of Mathematics, Polydisciplinary Faculty of Taza Sidi Mohammed Ben Abdellah University, Fez, Morocco
  • A. Boua Department of Mathematics, Polydisciplinary Faculty of Taza Sidi Mohammed Ben Abdellah University, Fez, Morocco

DOI:

https://doi.org/10.17398/2605-5686.38.1.51

Keywords:

3-prime near-rings, Jordan ideals, Left derivations

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.

References

M. Ashraf, N. Rehman, On Lie ideals and Jordan left derivation of prime rings, Arch. Math. (Brno) 36 (2000), 201 – 206.

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.

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.

A. Boua, H.E. Bell, Jordan ideals and derivations satisfying algebraic identities, Bull. Iranian Math. Soc. 44 (2018), 1543 – 1554.

A. Boua, L. Oukhtitei, A. Raji, Jordan ideals and derivations in prime near-rings, Comment. Math. Univ. Carolin. 55 (2) (2014), 131 – 139.

A. Boua, Commutativity of near-rings with certain constrains on Jordan ideals, Bol. Soc. Parana. Mat. (3) 36 (4) (2018), 159 – 170.

M. Brešar, J. Vukman, On left derivations and related mappings, Proc. Amer. Math. Soc. 110 (1) (1990), 7 – 16.

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.

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.

Downloads

Published

2023-01-23

Issue

Section

Algebras (associative, non associative, topological)

How to Cite

On Jordan ideals with left derivations in 3-prime near-rings. (2023). Extracta Mathematicae, 38(1), 51-66. https://doi.org/10.17398/2605-5686.38.1.51