Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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NOETHERIAN RINGS OF KRULL DIMENSION 2

  • Shin, Yong-Su (Department of Mathematics, Sungshin Women's University)
  • Received : 2010.01.18
  • Accepted : 2010.03.27
  • Published : 2010.05.30
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Abstract

We prove that a maximal ideal M of D[x] has two generators and is of the form where p is an irreducible element in a PID D having infinitely many nonassociate irreducible elements and q(x) is an irreducible non-constant polynomial in D[x]. Moreover, we find how minimal generators of maximal ideals of a polynomial ring D[x] over a DVR D consist of and how many generators those maximal ideals have.

Keywords

Acknowledgement

Supported by : Sungshin Women's University

References

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  3. J.J. Watkins, Topics in Commutative Ring Theory, Princeton University Press, (2007).
  4. F. Zanello, When Are There Infinitely Many Irreducible Elements in a Principal Ideal Domain?, American Mathematical Monthly, 111(2):150-152, (2004). https://doi.org/10.2307/4145215