# Bulletin of theKorean Mathematical SocietyBKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

## Article

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Bull. Korean Math. Soc. 2022; 59(2): 419-429

Published online March 31, 2022 https://doi.org/10.4134/BKMS.b210322

## Trace Properties and Integral Domains, III

Thomas G. Lucas, Abdeslam Mimouni

University of North Carolina Charlotte; King Fahd University of Petroleum and Minerals

### 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.

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.