East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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COMPOSITE HURWITZ RINGS AS ARCHIMEDEAN RINGS

  • Lim, Jung Wook (Department of Mathematics, Kyungpook National University)
  • Received : 2016.11.07
  • Accepted : 2017.05.08
  • Published : 2017.05.31
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Abstract

Let $D{\subseteq}E$ be an extension of integral domains with characteristic zero, I be a nonzero proper ideal of D, and let H(D, E) and H(D, I) (resp., h(D, E) and h(D, I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this article, we show that H(D, E) is an Archimedean ring if and only if h(D, E) is an Archimedean ring, if and only if ${\bigcap}_{n{\geq}1}d^nE=(0)$ for each nonzero nonunit d in D. We also prove that H(D, I) is an Archimedean ring if and only if h(D, I) is an Archimedean ring, if and only if D is an Archimedean ring.

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References

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