## Rocky Mountain Journal of Mathematics

- Rocky Mountain J. Math.
- Volume 46, Number 4 (2016), 1379-1393.

### Two sided $\alpha $-derivations in 3-prime near-rings

M. Samman, L. Oukhtite, A. Raji, and A. Boua

#### Abstract

The purpose of this paper is to investigate two sided $\alpha $-derivations satisfying certain differential identities on 3-prime near-rings. Some well-known results characterizing commutativity of 3-prime near-rings by derivations (semi-derivations) have been generalized. Furthermore, examples proving the necessity of the 3-primeness hypothesis are given.

#### Article information

**Source**

Rocky Mountain J. Math., Volume 46, Number 4 (2016), 1379-1393.

**Dates**

First available in Project Euclid: 19 October 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1476884588

**Digital Object Identifier**

doi:10.1216/RMJ-2016-46-4-1379

**Mathematical Reviews number (MathSciNet)**

MR3563187

**Zentralblatt MATH identifier**

1353.16018

**Subjects**

Primary: 16N60: Prime and semiprime rings [See also 16D60, 16U10] 16W25: Derivations, actions of Lie algebras 16Y30: Near-rings [See also 12K05]

**Keywords**

$3$-prime near-rings two sided $\alpha $-derivations commutativity

#### Citation

Samman, M.; Oukhtite, L.; Raji, A.; Boua, A. Two sided $\alpha $-derivations in 3-prime near-rings. Rocky Mountain J. Math. 46 (2016), no. 4, 1379--1393. doi:10.1216/RMJ-2016-46-4-1379. https://projecteuclid.org/euclid.rmjm/1476884588