The images of polynomials of derivations
Journal
Communications in Algebra
Journal Volume
45
Journal Issue
10
Pages
4550-4556
Date Issued
2017
Author(s)
Eroǧlu, M.P.
Abstract
Let R be a simple GPI-ring (i.e., a simple ring satisfying a nontrivial generalized polynomial identity) with a nonzero derivation δ and with Martindale symmetric ring of quotients Q. Motivated by the Noether-Skolem theorem, we characterize linear differential maps φ: x ↦ Σij aijδj(x)bij for x∈R, where aij, bij are finitely many elements in Q, such that ϕ(R)⊆[R,R]. The result is described and proved in terms of polynomials in Q[t;δ], the Ore extension of Q by the derivation δ.
Type
journal article