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A ring $R$ is called left GF-closed, if the class of all Gorenstein flat left$R$-modules is closed under extensions. The class of left GF-closed ringsincludes strictly the one of right coherent rings and the one of rings offinite weak dimension.  In this paper, we investigate the Gorenstein flat dimension over leftGF-closed rings. Namely, we generalize the fact that the class of allGorenstein flat left modules is projectively resolving over right coherentrings to left GF-closed rings. Also, we generalize the characterization ofGorenstein flat left modules (then of Gorenstein flat dimension of leftmodules) over right coherent rings to left GF-closed rings. Finally, usingdirect products of rings, we show how to construct a left GF-closed ring thatis neither right coherent nor of finite weak dimension.

Rings over which the class of Gorenstein flat modules is closed under extensions