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MiS Preprint

Noetherian operators, primary submodules and symbolic powers

Yairon Cid Ruiz


We give an algebraic and self-contained proof of the existence of the so-called Noetherian operators for primary submodules over general classes of Noetherian commutative rings. The existence of Noetherian operators accounts to provide an equivalent description of primary submodules in terms of differential operators. As a consequence, we introduce a new notion of differential powers which coincides with symbolic powers in many interesting non-smooth settings, and so it could serve as a generalization of the Zariski-Nagata Theorem.

Sep 17, 2019
Sep 23, 2019
MSC Codes:
13N10, 13N99, 13A15

Related publications

2021 Repository Open Access
Yairon Cid-Ruiz

Noetherian operators, primary submodules and symbolic powers

In: Collectanea mathematica, 72 (2021) 1, pp. 175-202