## Journal of Commutative Algebra

### Radical perfectness of prime ideals in certain integral domains

#### 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

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

#### 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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