Bull. Korean Math. Soc. 2022; 59(2): 419-429
Published online March 31, 2022 https://doi.org/10.4134/BKMS.b210322
Copyright © The Korean Mathematical Society.
Thomas G. Lucas, Abdeslam Mimouni
University of North Carolina Charlotte; King Fahd University of Petroleum and Minerals
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.
Keywords: Trace ideal, radical trace property, RTP domain, LTP domain
MSC numbers: Primary 13A15; Secondary 13F05, 13G05
Supported by: The second named author was supported by KFUPM under DSR Grant \#: SB181004.
2022 © The Korean Mathematical Society. Powered by INFOrang Co., Ltd