Simplicity of Some Derivations of k[x, y]

Abstract

If k is a field of characteristic zero, c ∈ k∖0, and 1 ≤ s ≤ r are integers such that either r − s + 1 divides s or s divides r − s + 1, then it is shown that the derivation y ^r ∂ _x  + (xy ^s  + c)∂ _y of the polynomial ring k[x, y] is simple.

Key Words:

• Derivations
• Simple derivation
• d-Simple ring

2010 Mathematics Subject Classification:

• 13N15
• 13C99

ACKNOWLEDGMENTS

First author is financially supported by CSIR, India.

Notes

Communicated by M. Bresar.