Two-Sided Ideals in Rings of Differential Operators and Étale Homomorphisms Original Research Article

Let A be a commutative Noetherian and reduced ring. If A has an étale covering B such that all the irreducible components of B are geometric unibranches, we will construct an invariant ideal γ(A) of A which has the following properties: If A is an algebra over some ring k, then γ(A) is an essential left image(A)-submodule of A, and if all the irreducible components of B have rings of differential operators that are simple, then γ(A) is the minimal essential left image(A)-submodule of A, and image(A, γ(A)) is the minimal essential two-sided ideal of image(A).