Algebraists asked whether or not an operator on the module of smooth sections of the tangent bundle over the commutative ring of smooth functions of a smooth (orientable) manifold (can be any piece of a compact or a complete manifold) can be characterized by two axioms. In this note we confirm this for any smooth manifold M M under the assumption that H 1 ( M , R ) = { 0 } H^1(M, \mathbb {R})=\{0\} .