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

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.