On Jordan left derivations and generalized Jordan left derivations of matrix rings

Document Type : Research Paper


Academic member of University of Kurdistan


Abstract. Let R be a 2-torsion free ring with identity. In this
paper, first we prove that any Jordan left derivation (hence, any left
derivation) on the full matrix ringMn(R) (n  2) is identically zero,
and any generalized left derivation on this ring is a right centralizer.
Next, we show that if R is also a prime ring and n  1, then any
Jordan left derivation on the ring Tn(R) of all n×n upper triangular
matrices over R is a left derivation, and any generalized Jordan left
derivation on Tn(R) is a generalized left derivation. Moreover, we
prove that any generalized left derivation on Tn(R) is decomposed
into the sum of a right centralizer and a Jordan left derivation.
Some related results are also obtained.


Main Subjects

Volume 38, Issue 3 - Serial Number 3
September 2012
Pages 689-698
  • Receive Date: 10 August 2010
  • Revise Date: 02 March 2011
  • Accept Date: 02 March 2011
  • First Publish Date: 15 September 2012