Taiwanese Journal of Mathematics

JORDAN DERIVATIONS OF SOME CLASSES OF MATRIX RINGS

Nader M. Ghosseiri

Full-text: Open access

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


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