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Noetherian operators, primary submodules and symbolic powers

Yairon Cid Ruiz (UGent)
(2021) COLLECTANEA MATHEMATICA. 72(1). p.175-202
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Abstract
We give an algebraic and self-contained proof of the existence of the so-calledNoetherian operatorsfor 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.
Keywords
Applied Mathematics, General Mathematics, Differential operators, Primary ideals, Primary submodules, Noetherian operators, Symbolic powers, Differential powers, DIFFERENTIAL-OPERATORS

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Citation

Please use this url to cite or link to this publication:

MLA
Cid Ruiz, Yairon. “Noetherian Operators, Primary Submodules and Symbolic Powers.” COLLECTANEA MATHEMATICA, vol. 72, no. 1, 2021, pp. 175–202, doi:10.1007/s13348-020-00285-3.
APA
Cid Ruiz, Y. (2021). Noetherian operators, primary submodules and symbolic powers. COLLECTANEA MATHEMATICA, 72(1), 175–202. https://doi.org/10.1007/s13348-020-00285-3
Chicago author-date
Cid Ruiz, Yairon. 2021. “Noetherian Operators, Primary Submodules and Symbolic Powers.” COLLECTANEA MATHEMATICA 72 (1): 175–202. https://doi.org/10.1007/s13348-020-00285-3.
Chicago author-date (all authors)
Cid Ruiz, Yairon. 2021. “Noetherian Operators, Primary Submodules and Symbolic Powers.” COLLECTANEA MATHEMATICA 72 (1): 175–202. doi:10.1007/s13348-020-00285-3.
Vancouver
1.
Cid Ruiz Y. Noetherian operators, primary submodules and symbolic powers. COLLECTANEA MATHEMATICA. 2021;72(1):175–202.
IEEE
[1]
Y. Cid Ruiz, “Noetherian operators, primary submodules and symbolic powers,” COLLECTANEA MATHEMATICA, vol. 72, no. 1, pp. 175–202, 2021.
@article{8681016,
  abstract     = {{We give an algebraic and self-contained proof of the existence of the so-calledNoetherian operatorsfor 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.}},
  author       = {{Cid Ruiz, Yairon}},
  issn         = {{0010-0757}},
  journal      = {{COLLECTANEA MATHEMATICA}},
  keywords     = {{Applied Mathematics,General Mathematics,Differential operators,Primary ideals,Primary submodules,Noetherian operators,Symbolic powers,Differential powers,DIFFERENTIAL-OPERATORS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{175--202}},
  title        = {{Noetherian operators, primary submodules and symbolic powers}},
  url          = {{http://dx.doi.org/10.1007/s13348-020-00285-3}},
  volume       = {{72}},
  year         = {{2021}},
}
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