Concerning the frame of minimal prime ideals of pointfree function rings
Abstract. Let L be a completely regular frame and RL be the ring of continuous real-valued functions on L. We study the frame O(Min(RL)) of minimal prime ideals of RL in relation to L. For I 2 L, denote by OI the ideal f 2 RL j coz 2 Ig of RL. We show that sending I to the set of minimal prime ideals not containing OI produces a -dense one-one frame homomorphism L ! O(Min(RL)) which is an isomorphism if and only if L is basically disconnected.
frame, ring of real-valued continuous functions on a frame, minimal prime ideal, basically disconnected. Subject Classication: 06D22, 54E17, 18A40. The author acknowledges nancial assistance from the National Research Foundation of South Africa.