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Let $R$ be a right and left Ore ring, $S$ its set of regular elements and $Q = R[S^{-1}] = [S^{-1}] R$ the classical ring of quotients of $R$. We prove that if $\Fdim(Q_Q) = 0$, then
the following conditions are equivalent:
$(i)$~Flat right
$R$-modules are strongly flat.
$ (ii)$ Matlis-cotorsion right $R$-modules are Enochs-cotorsion.
$(iii) $ $h$-divisible right $R$-modules are weak-injective.
$(iv)$~Homomorphic images of weak-injective right $R$-modules are weak-injective.
$(v)$ Homomorphic images of injective right $R$-modules are weak-injective.
$(vi)$~Right $R$-modules of weak dimension $ \le 1$ are of projective dimension $\le1$.
$(vii)$~The cotorsion pairs $(\Cal P_1,\Cal D)$ and $(\Cal F_1,\Cal W\Cal I)$ coincide.
$(viii)$ Divisible right $R$-modules are weak-injective. This extends a result by Fuchs and Salce (2018) [10] for modules over a commutative ring $R$.
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