Cozero complemented frames

The Tychonoff spaces X for which the minimal prime ideal space Min(C(X)) is compact have an internal characterization, namely that for every cozero set U of X there is a cozero set Vsuch that U∩V=∅ and U∪V is dense. For this reason they are called cozero complemented. In the setting of frames one also has that Min(RL) is compact precisely if for every c∈CozL, there is a d∈CozL with c∧d=0 and c∨d dense. Our aim in this paper is to examine how far the spatial characterizations extend to the larger terrain of pointfree topology.