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manuscripta mathematica

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

Symmetric semigroups of integers generated by 4 elements

  • H. Bresinsky
Article

Abstract

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.

Keywords

Number Theory Algebraic Geometry Nonnegative Integer Prime Ideal Topological Group 
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.

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References

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    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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