## 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