The $φ$-weak dimension of $φ$-pseudo-valuation rings - Kim, Hwankoo; Mahdou, Najib; Oubouhou, El Houssaine (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 512.5It is shown that, for a strongly $φ$-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the $φ$-weak global dimension are 0, 1, and $∞.$ We then provide necessary and sufficient conditions for a strongly $φ$-pseudo-valuation ring to be nonnil-coherent. As an application of these findings, we demonstrate that if $R$ is a strongly nonnil-coherent $φ$-pseudo-valuation ring, then any overring $B$ of $R$ is also a nonnil-coherent $φ$-pseudo-valuation ring.