TRACE PROPERTIES AND INTEGRAL DOMAINS, III

Thomas G. Lucas; Abdeslam Mimouni

doi:10.4134/BKMS.b210322

TRACE PROPERTIES AND INTEGRAL DOMAINS, III

Thomas G. Lucas
, Abdeslam Mimouni

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

An integral domain R is an RTP domain (or has the radical trace property) (resp. an LT P domain) if I(R: I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R: I)R_P = P R_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.

Original language	English
Pages (from-to)	419-429
Number of pages	11
Journal	Bulletin of the Korean Mathematical Society
Volume	59
Issue number	2
DOIs	https://doi.org/10.4134/BKMS.b210322
State	Published - 31 Mar 2022

Bibliographical note

Publisher Copyright:
© 2022 Korean Mathematial Soiety.

Keywords

LTP domain
RTP domain
Trace ideal
radical trace property

ASJC Scopus subject areas

General Mathematics

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10.4134/BKMS.b210322

Cite this

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abstract = "An integral domain R is an RTP domain (or has the radical trace property) (resp. an LT P domain) if I(R: I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R: I)RP = P RP 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 = "LTP domain, RTP domain, Trace ideal, radical trace property",

author = "Lucas, \{Thomas G.\} and Abdeslam Mimouni",

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doi = "10.4134/BKMS.b210322",

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N2 - An integral domain R is an RTP domain (or has the radical trace property) (resp. an LT P domain) if I(R: I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R: I)RP = P RP 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.

AB - An integral domain R is an RTP domain (or has the radical trace property) (resp. an LT P domain) if I(R: I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R: I)RP = P RP 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.

KW - LTP domain

KW - RTP domain

KW - Trace ideal

KW - radical trace property

UR - https://www.scopus.com/pages/publications/85128772945

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DO - 10.4134/BKMS.b210322

M3 - Article

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VL - 59

SP - 419

EP - 429

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 2

ER -

TRACE PROPERTIES AND INTEGRAL DOMAINS, III

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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