Differential simplicity and the module of derivations
Let \(A\) be a Noetherian local ring and \(D\subset \text{Der} (A)\) a finitely generated \(A\)-submodule, which is closed under Lie operation of derivations. If \(I\) is a maximally \(D\)-differential ideal then \(D/ID\) is free over \(A/I\). In particular, if \(A\) contains a field \(k\) such that \(D= \text{Der}_k (A)\) is finitely generated over \(A\) and \(A\) is differentially simple under \(D\) then \(D\) is free over \(A\).
scientific article; zbMATH DE number 986726