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Given a non-negative integer $n$ and a ring $R$ with identity, we constructan abelian model structure on the category of left $R$-modules where the classof cofibrant objects coincides with $\GF_n(R)$ the class of left $R$-moduleswith Gorenstein flat dimension less than $n$, the class of fibrant objectscoincides with $\flat_n(R)^\perp$ the right $\Ext$-orthogonal class of left$R$-modules with flat dimension less than $n$, and the class of trivial objectscoincides with $\PGF(R)^\perp$ the right $\Ext$-orthogonal class of PGF left$R$-modules recently introduced by \v{S}aroch and \v{S}\v{t}ov\'{\i}\v{c}ek.The homotopy category of this model structure is triangulated equivalent to thestable category $\underline{\GF(R)\cap\cot(R)}$ modulo flat-cotorsion modulesand it is compactly generated when $R$ has finite global Gorenstein projectivedimension.  The second part of this paper deals with the PGF dimension of modules andrings. Our results suggest that this dimension could serve as an alternativedefinition of the Gorenstein projective dimension. We show, among other things,that ($n$-)perfect rings can be characterized in terms of Gorensteinhomological dimensions, similar to the classical ones, and the globalGorenstein projective dimension coincides with the global PGF dimension.

Model structures, n-Gorenstein flat modules and PGF dimensions