The $\phi$-weak dimension of $\phi$-pseudo-valuation rings

• Date: 2026
• Main Authors: Kim, Hwankoo, Mahdou, Najib, Oubouhou, El Houssaine
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8299
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...