Note on Nilpotent Derivations
Resource
Proceedings of the American Mathematical Society,98(1),31-32.
Journal
Proceedings of the American Mathematical Society
Journal Volume
98
Journal Issue
1
Pages
31-32
Date Issued
1986-01
Date
1986-01
Author(s)
Abstract
Let R be a prime ring with center Z. Suppose that d is a derivation on R such that dn(x) ∈ Z for all x, where is a fixed integer. It is shown that either dnx 0 for all x ∈ R or R is a commutative integral domain. Moreover, the same conclusion holds even if we assume that dnx ∈ Z merely for all x ∈ I, where I is a nonzero ideal of R. © 1986 American Mathematical Society.
Type
journal article