Semistar operations on Dedekind domains

Details Semistar operations on Dedekind domains Semistar operations on Dedekind domains

2011-10-10

arxiv.org/abs/1110.1898v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

We give an explicit description of the lattice $\Semistar(D)$ of all semistar operations on any Dedekind domain $D$ from its set $\Max(D)$ of maximal ideals. This descpription is constructive if $\Max(D)$ is finite. As a corollary we show that $2^{{n \choose [n/2]}} \leq |\Semistar(D)| \leq 2^{2^n}$ if $n = |\Max(D)|$ is finite; we compute $|\Semistar(D)|$ if $|\Max(D)| \leq 7$; and we show that if $\Max(D)$ is infinite then $\Semistar(D)$ has cardinality $2^{2^{|\Max(D)|}}$.

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