manuscripta mathematica

, Volume 17, Issue 3, pp 205–219 | Cite as

Symmetric semigroups of integers generated by 4 elements

  • H. Bresinsky


Let K be an arbitrary field, t transcendental over over K. It is shown that if the numerical semigroup of nonnegative integers, generated nonredundantly by 4 elements, is symmetric, then the prime ideal of all polynomials f(x1,x2,X3,x4) ε K[x1,x2,x3,x4] such that\(f(t^{n_1 } ,t^{n_2 } ,t^{n_3 } ,t^{n_4 } ) = 0\) is generated by 3 or 5 elements. From this, arithmetic conditions for the generators are obtained.


Number Theory Algebraic Geometry Nonnegative Integer Prime Ideal Topological Group 
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  1. [1]
    APERY, R.: Sur les branches superlinéaires des courbes algebriques. C. R. Acad. Sci. Paris 222, 1198–1200 (1946).Google Scholar
  2. [2]
    BRESINSKY, H.: Semigroup and analytic equivalence of algebroid branches in the plane. Thesis, Arizona State University, Tempe, Arizona (1969).Google Scholar
  3. [3]
    BRESINSKY, H.: On prime ideals with generic zero\(x_i = t^{n_i }\). Proc. Amer. Math. Soc. 47, 329–332 (1975).Google Scholar
  4. [4]
    HERZOG, J.: Generators and relations of abelian semigroups and semigroup rings. manuscripta math. 3, 175–193 (1970).Google Scholar
  5. [5]
    WATANABE, K.: Some examples of one dimensional Gorenstein domains. Nagoya Math. J. 49, 101–109 (1973).Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • H. Bresinsky
    • 1
  1. 1.Department of MathematicsUniversity of Maine at OronoOrono

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