Noetherian operators, primary submodules and symbolic powers
Yairon Cid Ruiz
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Submission date: 17. Sep. 2019
published in: Collectanea mathematica (2020), pp not yet known
DOI number (of the published article): 10.1007/s13348-020-00285-3
MSC-Numbers: 13N10, 13N99, 13A15
Link to arXiv: See the arXiv entry of this preprint.
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.