## Taiwanese Journal of Mathematics

- Taiwanese J. Math.
- Volume 11, Number 1 (2007), 51-62.

### JORDAN DERIVATIONS OF SOME CLASSES OF MATRIX RINGS

#### Abstract

Let $R$ be a 2-torsionfree ring with identity and $S$ be a subring of the ring $M_n(R)$ that contains the ring $T_n(R)$ of all upper triangular matrices over $R$; that is, $T_n(R) \subseteq S \subseteq M_n(R)$. The goal of this paper is to describe a Jordan derivation $\Delta$ on $S$. The main result states that $\Delta$ can be uniquely represented as the sum of a derivation and a very special Jordan derivation. This result describes also the structure of every derivation on the ring $S$ which is an extension of a result of S.P. Coelho and C.P. Milies and a result of $S$. Jøndrup. Moreover, one of the corollaries of the main theorem covers the classical result by Jacobson and Rickart stating that there are no proper Jordan derivations on $M_n(R)$, and a more recent result by D. Benkovic that there are no proper Jordan derivations on the algebra $T_n(R)$.

#### Article information

**Source**

Taiwanese J. Math., Volume 11, Number 1 (2007), 51-62.

**Dates**

First available in Project Euclid: 18 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.twjm/1500404633

**Digital Object Identifier**

doi:10.11650/twjm/1500404633

**Mathematical Reviews number (MathSciNet)**

MR2304004

**Zentralblatt MATH identifier**

1142.16024

**Subjects**

Primary: 16W25: Derivations, actions of Lie algebras

**Keywords**

derivation antiderivation Jordan derivation matrix ring

#### Citation

Ghosseiri, Nader M. JORDAN DERIVATIONS OF SOME CLASSES OF MATRIX RINGS. Taiwanese J. Math. 11 (2007), no. 1, 51--62. doi:10.11650/twjm/1500404633. https://projecteuclid.org/euclid.twjm/1500404633