Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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FINITELY t-VALUATIVE DOMAINS

  • Chang, Gyu Whan (Department of Mathematics Education Incheon National University)
  • Received : 2014.09.06
  • Accepted : 2014.09.16
  • Published : 2014.12.30
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Abstract

Let D be an integral domain with quotient field K. In [1], the authors called D a finitely valuative domain if, for each $0{\neq}u{\in}K$, there is a saturated chain of rings $D=D_0{\varsubsetneq}D_1{\varsubsetneq}{\cdots}{\subseteq}$ $D_n=D[x]$, where x = u or $u^{-1}$. They then studied some properties of finitely valuative domains. For example, they showed that the integral closure of a finitely valuative domain is a Pr$\ddot{u}$fer domain. In this paper, we introduce the notion of finitely t-valuative domains, which is the t-operation analog of finitely valuative domains, and we then generalize some properties of finitely valuative domains.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

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