  In this paper, we investigate the weak Gorenstein global dimensions. We are
mainly interested in studying the problem when the left and right weak
Gorenstein global dimensions coincide. We first show, for GF-closed rings, that
the left and right weak Gorenstein global dimensions are equal when they are
finite. Then, we prove that the same equality holds for any two-sided coherent
ring. We conclude the paper with some examples and a brief discussion of the
scope and limits of our results.
