The first Hochschild cohomology as a Lie algebra

On the Lie algebra structure of integrable derivations

“…It is easy to show that a $$[1,\infty ]$$‐integrable derivation is $$[m,\infty ]$$‐integrable for every $$m$$ (see [27, Theorem 3.6.6]). The next result of Gerstenhaber's shows that the converse is also true.…”

“…By Lemma 1, we may assume that 𝑘 is an algebra over ℤ 𝑝 , so that the results of [10] apply. As Der(𝐴) is an Artinian 𝑘-module, the sequence of submodules Der [1,𝑛) (𝐴) must eventually stabilise, and so there is an [27,Theorem 3.6.6]). The next result of Gerstenhaber's shows that the converse is also true.…”