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Prime Galois connections. (English) Zbl 1240.06013

Summary: It is known that the set \({\mathcal G}(P,Q)\) of Galois connections of a complete Heyting algebra \(P\) into an algebraic lattice \(Q\) forms a complete lattice. Here we introduce binary operations on \({\mathcal G}(P,Q)\) corresponding to those on \(Q\) as their natural extensions and discuss certain important properties of them. In particular, the prime, minimal and maximal elements of \({\mathcal G}(P,Q)\) are characterized in terms of those in \(Q\).

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
06B23 Complete lattices, completions
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