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Ideals of quantales. (Chinese. English summary) Zbl 1045.06007

Summary: A (left, right) ideal of a quantale \(Q\) is introduced and the concrete structure of the (left, right) ideal generated by a given set is considered. The relation between an ideal of a quantale \(Q\) and the corresponding ideal of the lattice \(Q\) is studied. A necessary and sufficient condition for an element of \(\text{Id}(Q)\) to be idempotent is obtained if the quantale \(Q\) is commutative.

MSC:

06F07 Quantales
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