Journal of Commutative Algebra

Radical perfectness of prime ideals in certain integral domains

Gyu Whan Chang and Hwankoo Kim

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Abstract

For a UMT-domain $D$, we characterize when the polynomial ring $D[X]$ is $t$-compactly packed and every prime $t$-ideal of $D[X]$ is radically perfect. As a corollary, for a quasi-Pr\"ufer domain $D$, we also characterize when every prime ideal of $D[X]$ is radically perfect. Finally we introduce the concepts of Serre's conditions in strong Mori domains and characterize Krull domains and almost factorial domains, respectively.

Article information

Source
J. Commut. Algebra, Volume 9, Number 1 (2017), 31-48.

Dates
First available in Project Euclid: 5 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.jca/1491379318

Digital Object Identifier
doi:10.1216/JCA-2017-9-1-31

Mathematical Reviews number (MathSciNet)
MR3631825

Zentralblatt MATH identifier
1364.13005

Subjects
Primary: 13A15: Ideals; multiplicative ideal theory 13E99: None of the above, but in this section 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 13G05: Integral domains

Keywords
Prüfer domain radically perfect $t$-compactly packed quasi-Prüfer domain UMT-domain SM domain Serre's condition

Citation

Chang, Gyu Whan; Kim, Hwankoo. Radical perfectness of prime ideals in certain integral domains. J. Commut. Algebra 9 (2017), no. 1, 31--48. doi:10.1216/JCA-2017-9-1-31. https://projecteuclid.org/euclid.jca/1491379318


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