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 \(|\mathrm{SStar}(D)|=2^{2^{|\mathrm{Max}(D)|}}\).


13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
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