Trace Properties and Integral Domains, III
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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.
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.~$I(R:I)R_P=PR_P$ 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.
참고문헌 (14)
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