Local Derivations of Ore Extensions of the Polynomial Ring in One Variable

Abstract

Let R[t, d] be an Ore extension where R is a polynomial ring in one variable over a field of characterstic zero. We prove that every local derivation of R[t, d] is a derivation.

Key Words:

• Derivation
• Local derivation
• Ore extension
• Skew polynomial ring
• Weyl algebra
• Kadison algebra

Mathematics Subject Classification:

• Primary 16W25, 16S36
• Secondary 47B47

Acknowledgment

The author wish to thank the referee for his helpful remarks and for writing a very constructive report.

Notes

^#Communicated by J. Kuzmanovich.