Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON GENERALIZED KRULL POWER SERIES RINGS

  • Le, Thi Ngoc Giau (Faculty of Mathematics and Statistics Ton Duc Thang University) ;
  • Phan, Thanh Toan (Faculty of Mathematics and Statistics Ton Duc Thang University)
  • Received : 2017.03.16
  • Accepted : 2017.09.14
  • Published : 2018.07.31
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Abstract

Let R be an integral domain. We prove that the power series ring R[[X]] is a Krull domain if and only if R[[X]] is a generalized Krull domain and t-dim $R{\leq}1$, which improves a well-known result of Paran and Temkin. As a consequence we show that one of the following statements holds: (1) the concepts "Krull domain" and "generalized Krull domain" are the same in power series rings, (2) there exists a non-t-SFT domain R with t-dim R > 1 such that t-dim R[[X]] = 1.

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References

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