Concerning the frame of minimal prime ideals of pointfree function rings

Let L be a completely regular frame and RL be the ring of continuous real-valued functions on L. We study the frame σ(Min(RL)) of minimal prime ideals of RL in relation to βL. For I ∈ βL, denote by O^I the ideal {α ∈ RL j coz α ∈ I of RL}. We show that sending I to the set of minimal prime ideals not containing O^I produces a *-dense one-one frame homomorphism βL→ σ(Min(RL)) which is an isomorphism if and only if L is basically disconnected.