manuscripta mathematica

, Volume 29, Issue 2–4, pp 159–181 | Cite as

Monomial Gorenstein ideals

  • Henrik Bresinsky


The paper concerns itself with generating sets for monomial Gorenstein ideals in polynomial rings k[x1,..., xr], k an arbitrary field. For r=5 it is shown that for a certain class of these ideals, the number of generators is bounded by 13. To establish the sharpness of this bound an algorithm is established, to obtain all numerical symmetric semigroups with a fixed odd integer 2n+1 as last integer unattained. Finally, a short proof of the known fact is given, that for r=4 the number of elements in a generating set is 3 or 5.


Number Theory Algebraic Geometry Topological Group Polynomial Ring Short Proof 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    ANGERMÜLLER, G.: Die Wertehalbgruppe einer ebenen irreduziblen Kurve, Math. Z.153, 267–282 (1977)Google Scholar
  2. [2]
    APÉRY, R.: Sur les branches superlinéaires des courbes algebriques, C. R. Acad. Sci. Paris222, 1198–1200 (1946)Google Scholar
  3. [3]
    BRESINSKY, H.: Semigroups corresponding to algebroid branches in the plane, Proc. Amer. Math. Soc.32, 381–384 (1972)Google Scholar
  4. [4]
    BRESINSKY, H.: On prime ideals with generic zero\(x_i = t^{n_i }\), Proc. Amer. Math. Soc.47, 329–332 (1975)Google Scholar
  5. [5]
    BRESINSKY H.: Symmetric semigroups of integers generated by 4 elements, manuscripta math.17, 205–219 (1975)Google Scholar
  6. [6]
    BRESINSKY, H., FULLER, M. J.: Minimal bases of polynomial ideals, Houston J. of Math.3, 453–457 (1977)Google Scholar
  7. [7]
    HERZOG, J.: Generators and relations of Abelian semigroups and semigroup rings, manuscripta math.3, 175–193 (1970)Google Scholar
  8. [8]
    HERZOG, J., KUNZ, E.: Die Wertelhalbgruppe eines lokalen Rings der Dimension l, Ber. Heidelberger Akad. Wiss. 1971, II Abh. (1971)Google Scholar
  9. [9]
    GRAUERT H., REMMERT, R.: Analytische Stellenalgebren, Berlin-New York: Springer-Verlag 1971Google Scholar
  10. [10]
    KUNZ, E.: Almost complete intersections are not Gorenstein rings, J. of Algebra28, 111–115 (1974)Google Scholar
  11. [11]
    RENSCHUCH, B.: Beiträge zur konstruktiven Theorie der Polynomideale VI, Veronesesche Projektionskurven im S3, Wiss. Z. Päd. Hochschule “Karl Liebknecht”18, 100–106 (1974)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Henrik Bresinsky
    • 1
  1. 1.University of Maine at OronoOrono

Personalised recommendations