LOCALLY DIVIDED DOMAINS OF THE FORM $D[X]_N_v$

  • Chang, Gyu Whan (Department of Mathematics University of Incheon)
  • Received : 2009.12.22
  • Accepted : 2010.03.05
  • Published : 2010.03.01

Abstract

Let D be an integral domain, X be an indeterminate over D, and $N_v=\{f{\in}D[X]{\mid}(A_f)_v=D\}$. In this paper, we introduce the concept of t-locally divided domains, and we then prove that $D[X]_{N_v}$ is a locally divided domain if and only if D is a t-locally divided UMT-domain, if and only if D[X] is a t-locally divided domain.

Acknowledgement

Supported by : University of Incheon

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