The $\phi$-weak dimension of $\phi$-pseudo-valuation rings
UDC 512.5 It is shown that, for a strongly $\phi$-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the $\phi$-weak global dimension are 0, 1, and $\infty.$ We then provide necessary and sufficient conditions for a strongly $\phi$-pseudo-valuation ring to be nonnil-coheren...
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| Datum: | 2026 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8299 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 512.5
It is shown that, for a strongly $\phi$-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the $\phi$-weak global dimension are 0, 1, and $\infty.$ We then provide necessary and sufficient conditions for a strongly $\phi$-pseudo-valuation ring to be nonnil-coherent. As an application of these findings, we demonstrate that if $R$ is a strongly nonnil-coherent $\phi$-pseudo-valuation ring, then any overring $B$ of $R$ is also a nonnil-coherent $\phi$-pseudo-valuation ring. |
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| DOI: | 10.3842/umzh.v77i8.8299 |