  Distinctive characteristics of Iwanaga--Gorenstein rings are typically
understood through their intrinsic symmetry. We show that several of those that
pertain to the Gorenstein global dimensions carry over to the one-sided
situation, even without the noetherian hypothesis. Our results yield new
relations among homological invariants related to the Gorenstein property, not
only Gorenstein global dimensions but also the suprema of projective/injective
dimensions of injective/projective modules and finitistic dimensions.
