A note on ϕ-Prüfer v-multiplication rings

2021/07/25 by Xiaolei Zhang, Zhang, Xiaolei
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2107.11907

openalex publication_date 2021/07/25 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28

Abstract

In this note, we show that a strongly ϕ-ring R is a ϕ-PvMR if and only if any ϕ-torsion free R-module is ϕ-w-flat, if and only if any divisible module is nonnil-absolutely w-pure module, if and only if any h-divisible module is nonnil-absolutely w-pure module, if and only if any finitely generated nonnil ideal of R is w-projective.

Citations

• Two generalizations of projective modules and their applications

Related

• On strongly ϕ-w-Flat modules and Their Homological Dimensions
• Semi-regular flat modules over strong Prüfer rings
• A homological characterization of Q₀-Prüfer v-multiplication rings
• Module-Theoretic Characterizations of Prufer v-Multiplication Domains
• A new version of P-flat modules and its applications