East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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THE COHEN TYPE THEOREM FOR S-⁎ω-PRINCIPAL IDEAL DOMAINS

  • Lim, Jung Wook (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
  • Received : 2018.01.29
  • Accepted : 2018.07.04
  • Published : 2018.09.30
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Abstract

Let D be an integral domain, ${\ast}$ a star-operation on D, and S a (not necessarily saturated) multiplicative subset of D. In this article, we prove the Cohen type theorem for $S-{\ast}_{\omega}$-principal ideal domains, which states that D is an $S-{\ast}_{\omega}$-principal ideal domain if and only if every nonzero prime ideal of D (disjoint from S) is $S-{\ast}_{\omega}$-principal.

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Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

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