Journal of Commutative Algebra

Radical perfectness of prime ideals in certain integral domains

Gyu Whan Chang and Hwankoo Kim

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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.

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

First available in Project Euclid: 5 April 2017

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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

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


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.

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