Strongly $\phi$-flat modules, strongly nonnil-injective modules and their homological dimensions

TL;DR

This paper introduces new classes of modules called strongly φ-flat and strongly nonnil-injective, explores their homological dimensions, and characterizes certain rings using these concepts.

Contribution

It presents novel definitions of strongly φ-flat and strongly nonnil-injective modules and provides homological characterizations of φ-Dedekind and φ-Prufer rings.

Findings

Defined strongly φ-flat and strongly nonnil-injective modules.

Analyzed homological dimensions related to these modules.

Characterized φ-Dedekind and φ-Prufer rings using these notions.

Abstract

In this paper, we first introduce and study the notions of strongly $\phi$-flat modules and strongly nonnil-injective modules. And then, we investigate the homology dimensions of modules and rings in terms of these two notions. Finally we give a new homological characterizations of $\phi$-Dedekind rings and $\phi$-\Prufer\ rings.