Advertisement

Ukrainian Mathematical Journal

, Volume 62, Issue 4, pp 530–536 | Cite as

Cubic rings and their ideals

  • Yu. A. Drozd
  • R. V. Skuratovskii
Article
  • 32 Downloads

We give an explicit description of cubic rings over a discrete valuation ring, as well as the description of all ideals of these rings.

Keywords

Commutative Ring Complete Intersection Primitive Idempotent Discrete Valuation Ring Geometric Nature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Y. A. Drozd and A. V. Roiter, “Commutative rings with finitely many integral indecomposable representations,” Izv. Akad. Nauk SSSR, Ser. Mat., 31, 783–798 (1967).zbMATHMathSciNetGoogle Scholar
  2. 2.
    A. Schappert, “A characterization of strictly unimodal plane curve singularities,” Lect. Notes Math., 1273, 168–177 (1987).CrossRefMathSciNetGoogle Scholar
  3. 3.
    C. T. C. Wall, “Classification of unimodal isolated singularities of complete intersections,” Proc. Symp. Pure Math., 40, No. 2, 625–640 (1983).Google Scholar
  4. 4.
    V. I. Arnold, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Maps, Vol. 1, Nauka, Moscow (1982).Google Scholar
  5. 5.
    Y. A. Drozd and G.-M. Greuel, On Schappert Characterization of Unimodal Plane Curve Singularities, The Brieskorn Anniversary Volume, Birkhäuser (1998), pp. 3–26.Google Scholar
  6. 6.
    Y. A. Drozd and G.-M. Greuel, “Cohen–Macaulay module type,” Compos. Math., 89, 315–338 (1993).zbMATHMathSciNetGoogle Scholar
  7. 7.
    R. B. Skuratovskii, “Ideals of one-branched singularities of curves of type W ,” Ukr. Mat. Zh., 61, No. 9, 1257–1266 (2009).Google Scholar
  8. 8.
    Y. A. Drozd, “On the existence of maximal orders,” Mat. Zametki, 37, 313–315 (1985).MathSciNetGoogle Scholar
  9. 9.
    D. K. Faddeev, “Introduction to the multiplicative theory of modules of integral representations,” Tr. Mat. Inst. Steklova, 80, 145–182 (1965).zbMATHMathSciNetGoogle Scholar
  10. 10.
    D. K. Faddeev, “On the theory of cubic Z-rings,” Tr. Mat. Inst. Steklova, 80, 183–187 (1965).zbMATHMathSciNetGoogle Scholar
  11. 11.
    Y. A. Drozd, “Ideals of commutative rings,” Mat. Sb., 101, 334–348 (1976).MathSciNetGoogle Scholar
  12. 12.
    H. Jacobinski, “Sur les ordres commutatifs avec un nombre fini de réseaux indécomposables,” Acta Math., 118, 1–31 (1967).zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Y. A. Drozd, “Cohen–Macaulay modules over Cohen–Macaulay algebras,” CMS Conf. Proc., 19, 25–53 (1996).MathSciNetGoogle Scholar
  14. 14.
    H. Bass, “On the ubiquity of Gorenstein rings,” Math. Z., 82, 8–28 (1963).zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Y. A. Drozd and G.-M. Greuel, “ Semi-continuity for Cohen–Macaulay modules,” Math. Ann., 306, 371–389 (1996).zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • Yu. A. Drozd
    • 1
  • R. V. Skuratovskii
    • 2
  1. 1.Institute of Mathematics, Ukrainian National Academy of SciencesKyivUkraine
  2. 2.Shevchenko Kyiv National UniversityKyivUkraine

Personalised recommendations