On rings with finite one-sided Gorenstein weak global dimension

Let [Formula: see text] be a ring over which the supremum of flat dimensions of all injective left [Formula: see text]-modules is finite. It is shown that a left [Formula: see text]-module is Gorenstein injective if and only if it is strongly cotorsion, which provides some characterizations of Gorenstein injective and Ding injective modules. As applications, we obtain that the class of all weak Gorenstein FP-injective modules forms a right-hand class of complete and hereditary cotosion pair and is closed under direct limits under coherent assumption.