Skip to main content
SpringerLink
Log in

Derivations and rational powers of ideals

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

If A is a commutative Noetherian ring and \(\delta \) is a derivation on A, we study the integral closure, coefficient ideals, and rational powers of the ideals I of A satisfying \(\delta (I)\subseteq I\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ciupercă, C.: First coefficient ideals and the \({\rm S}_2\)-ification of a Rees algebra. J. Algebra 242, 782–794 (2001)

    Article  MathSciNet  Google Scholar 

  2. Ciupercă, C.: Integral closure of strongly Golod ideals. Nagoya Math. J. https://doi.org/10.1017/nmj.2019.22 (to appear)

  3. Corso, A., Polini, C., Vasconcelos, W.V.: Multiplicity of the special fiber of blowups. Math. Proc. Camb. Philos. Soc. 140, 207–219 (2006)

    Article  MathSciNet  Google Scholar 

  4. Grayson, D.R., Stillman, M.E.: Macaulay2, a software system for research in algebraic geometry. https://www.math.uiuc.edu/Macaulay2/

  5. Grothendieck, A., Dieudonné, J.A.: Eléments de géométrie algébrique. I. Springer, Berlin (1971)

    MATH  Google Scholar 

  6. Hochster, M., Huneke, C.: Indecomposable canonical modules and connectedness. Commutative Algebra: Syzygies. Multiplicities, and Birational Algebra, Volume 159 of Contemporary Mathematics, pp. 197–208. American Mathematical Society, Providence (1994)

  7. Huneke, C., Swanson, I.: Integral Closure of Ideals, Rings, and Modules. Cambridge University Press, Cambridge (2006)

    MATH  Google Scholar 

  8. Miranda-Neto, C.B.: Tangential idealizers and differential ideals. Collect. Math. 67, 311–328 (2016)

    Article  MathSciNet  Google Scholar 

  9. Ratliff Jr., L.J., Rush, D.E.: Two notes on reductions of ideals. Indiana Univ. Math. J. 27, 929–934 (1978)

    Article  MathSciNet  Google Scholar 

  10. Seidenberg, A.: Derivations and integral closure. Pac. J. Math. 16, 167–173 (1966)

    Article  MathSciNet  Google Scholar 

  11. Seidenberg, A.: Differential ideals in rings of finitely generated type. Am. J. Math. 89, 22–42 (1967)

    Article  MathSciNet  Google Scholar 

  12. Shah, K.: Coefficient ideals. Trans. Am. Math. Soc. 327, 373–384 (1991)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics 2750, North Dakota State University, PO Box 6050, Fargo, ND,  58108-6050, USA

    Cătălin Ciupercă

Authors
  1. Cătălin Ciupercă
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cătălin Ciupercă.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ciupercă, C. Derivations and rational powers of ideals. Arch. Math. 114, 135–145 (2020). https://doi.org/10.1007/s00013-019-01388-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-019-01388-5

Keywords

Mathematics Subject Classification

Search

Navigation