Details

Autor(en) / Beteiligte

• Cid-Ruiz, Yairon

Titel

Noetherian operators, primary submodules and symbolic powers

Ist Teil von

• Collectanea mathematica (Barcelona), 2021-01, Vol.72 (1), p.175-202

Ort / Verlag

Milan: Springer Milan

Erscheinungsjahr

2021

Link zum Volltext

Quelle

SpringerLink

Beschreibungen/Notizen

• 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.