On Rings with Locally Nilpotent Skew Derivations

Abstract

In this article, we examine algebras with a locally nilpotent q-skew σ-derivation d when there is an element x such that d(x) = 1 and either q is not a root of 1 or q = 1 in characteristic zero. When characteristic p > 0, we also examine the situation where d is an ordinary derivation.

Key Words:

• Locally nilpotent
• Skew derivations

2000 Mathematics Subject Classification:

• 16A05
• 16W60

ACKNOWLEDGMENT

The second author's research was supported in part by Grant MNiSW nr N N201 268435. Much of the research was done while he was a visitor at DePaul University, and he thanks them for their hospitality.

Notes

Communicated by M. Bresar.