On strongly $\phi$-$w$-Flat modules and Their Homological Dimensions

TL;DR

This paper introduces the concept of strongly φ-w-flat modules, explores the φ-w-weak global dimension of NP-rings, and characterizes φ-Prüfer v-multiplication strongly φ-rings through these modules.

Contribution

It defines strongly φ-w-flat modules, studies the φ-w-weak global dimension of NP-rings, and characterizes φ-Prüfer v-multiplication strongly φ-rings using these modules.

Findings

Introduction of strongly φ-w-flat modules

Definition and analysis of φ-w-weak global dimension for NP-rings

Characterization of φ-Prüfer v-multiplication strongly φ-rings

Abstract

In this paper, we introduce and study the notion of strongly $\phi$-$w$-flat modules. The $\phi$-$w$-weak global dimension $\phi$-$w$-w.gl.dim$(R)$ of an NP-ring $R$ is also introduced and studied. We characterize $\phi$-\Prufer\ $v$-multiplication strongly $\phi$-rings in terms of strongly $\phi$-$w$-flat modules.