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

Abstract

In this paper, we first introduce and study the notions of strongly $\varphi$-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 $\varphi$-Dedekind rings and $\varphi$-\Prufer\ rings.

arXiv commentAdd Theorem 1.8. arXiv admin note: text overlap with arXiv:2107.12643