East Asian mathematical journal

  • 제33권3호
  • /
  • Pages.317-322
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  • 2017
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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COMPOSITE HURWITZ RINGS AS ARCHIMEDEAN RINGS

  • Lim, Jung Wook (Department of Mathematics, Kyungpook National University)
  • 투고 : 2016.11.07
  • 심사 : 2017.05.08
  • 발행 : 2017.05.31
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초록

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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참고문헌

  1. A. Benhissi and F. Koja, Basic properties of Hurwitz series rings, Ric. Mat. 61 (2012), 255-273. https://doi.org/10.1007/s11587-012-0128-2
  2. T. Dumitrescu, S.O. Ibrahim Al-Salihi, N. Radu, and T. Shah, Some factorization prop-erties of composite domains A + XB[X] and A + $XB{\mathbb{[}}{\mathbb{]}}$, Comm. Algebra 28 (2000), 1125-1139. https://doi.org/10.1080/00927870008826885
  3. A. Hurwitz, Sur un theoreme de M. Hadamard, C. R. Acad. Sci. Paris Ser. I Math. 128 (1899), 350-353.
  4. W.F. Keigher, On the ring of Hurwitz series, Comm. Algebra 25 (1997), 1845-1859. https://doi.org/10.1080/00927879708825957
  5. J.W. Lim and D.Y. Oh, Composite Hurwitz rings satisfying the ascending chain condition on principal ideals, Kyungpook Math. J. 56 (2016), 1115-1123. https://doi.org/10.5666/KMJ.2016.56.4.1115