Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HIGH DIMENSION PRUFER DOMAINS OF INTEGER-VALUED POLYNOMIALS

  • Cahen, Paul-Jean (Department of Mathematics, Universite d’Aix-Marseille III, CNRS UMR 6632, France) ;
  • Chabert, Jean-Luc (Department of Mathematics, CNRS FRE 2270, Universite de Picardie 80039 Amiens, France) ;
  • K.Alan Loper (Department of Mathematics, Ohio State University, Newark, USA)
  • Published : 2001.09.01
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Abstract

Let V be any valuation domain and let E be a subset of the quotient field K of V. We study the ring of integer-valued polynomials on E, that is, Int(E, V)={f$\in$K[X]｜f(E)⊆V}. We show that, if E is precompact, then Int(E, V) has many properties similar to those of the classical ring Int(Z).In particular, Int(E, V) is dense in the ring of continuous functions C(E, V); each finitely generated ideal of Int(E, V) may be generated by two elements; and finally, Int(E, V) is a Prufer domain.

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References

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