In this paper, we investigate the homological properties of n-coherent rings and extend several classical results to this framework. An n-coherent ring, for \(n \in \mathbb {N}^* \cup \{\infty \}\) , is defined by the property that every finitely generated submodule of a free module with projective dimension at most \(n-1\) is finitely presented. We introduce the concepts of n-flat and n-FP-injective modules, exploring their implications for the structure of n-coherent rings. Through the development of n-flat dimensions and n-weak global dimensions, we provide new characterizations of n-semihereditary and n-von Neumann regular rings. Additionally, we investigate quasi-perfect rings and confirm that weak n-von Neumann regular rings are quasi-perfect, thereby answering an open question posed by Mahdou. These results broaden the understanding of coherence and flatness in commutative algebra, linking these properties to projectivity and injectivity in novel ways.
