Derivations of Rings of Infinite Matrices

Abstract

For any associative unital ring R we investigate two rings – the ring of all infinite upper triangular matrices and the ring of all infinite matrices with the finite number of nonzero entries in each column. We describe derivations of these rings. We prove that every derivation of any of them is a sum of an inner derivation and a derivation which is induced by some derivation of R.

Key Words:

• Infinite matrices
• Ring derivations

2010 Mathematics Subject Classification:

• 16S32
• 16D99

Notes

Communicated by S. Sehgal.