The φ-weak dimension of φ-pseudo-valuation rings

UDC 512.5 It 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.