Characterizations of a *-Almost Distributive Lattice

The space of minimal prime ideals of an almost distributive lattice (ADL) with zero, endowed with the hull kernel topology is shown to be a zero-dimensional, totally disconnected Tychonoff space. Several characterizations of a ∗-ADL using the topological properties of the space of minimal prime ideals are obtained. Necessary and sufficient conditions for the space of minimal prime ideals of an ADL and the space of minimal prime ideals of its distributive lattice of all ideals, to be homeomorphic are furnished.