## Semistar operations on Dedekind domains.(English)Zbl 1321.13009

The author proves that the lattice $$\mathrm{SStar}(D)$$ of semistar operations on a Dedekind domain $$D$$ depends only on the cardinality of the set $$\mathrm{Max}(D)$$ of maximal ideals of $$D$$. Among others, he computes the cardinality $$|\mathrm{SStar}(D)|$$ of $$\mathrm{SStar}(D)$$ if $$|\mathrm{Max}(D)|\leq 7$$ and he shows that if $$\mathrm{Max}(D)$$ is infinite, then $$|\mathrm{SStar}(D)|=2^{2^{|\mathrm{Max}(D)|}}$$.

### MSC:

 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
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### References:

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