Let be the system of all distributive lattices and let be the system of all such that possesses the least element. Further, let be the system of all infinitely distributive lattices belonging to . In the present paper we investigate the radical classes of the systems , and .
We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that the class of affine complete bounded distributive lattices is closed under products and free products. We show that every (not necessarily bounded) distributive lattice can be embedded in an affine complete one and that ℚ ∩ [0, 1] is initial in the class of affine complete lattices.