• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.419-429
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• 2022

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)R_P = PR_P 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.