Concerning the frame of minimal prime ideals of pointfree function rings

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Abstract


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.

Keywords


frame, ring of real-valued continuous functions on a frame, minimal prime ideal, basically disconnected. Subject Classication[2000]: 06D22, 54E17, 18A40. The author acknowledges nancial assistance from the National Research Foundation of South Africa.

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References


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Themba Dube, Department of Mathematical Sciences, University of South Africa, P.O.

Box 392, 0003 Unisa, South Africa.

Email: dubeta@unisa.ac.za


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