Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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TRACE PROPERTIES AND INTEGRAL DOMAINS, III

  • Lucas, Thomas G. (Department of Mathematics and Statistics University of North Carolina Charlotte) ;
  • Mimouni, Abdeslam (Department of Mathematics King Fahd University of Petroleum and Minerals)
  • Received : 2021.04.20
  • Accepted : 2021.10.14
  • Published : 2022.03.31
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Abstract

An integral domain R is an RTP domain (or has the radical trace property) (resp. an LTP domain) if I(R : I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R : I)RP = PRP for each minimal prime P of I(R : I)). Clearly each RTP domain is an LTP domain, but whether the two are equivalent is open except in certain special cases. In this paper, we study the descent of these notions from particular overrings of R to R itself.

Keywords

Acknowledgement

The second named author was supported by KFUPM under DSR Grant #: SB181004.

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