Elliott, Jesse Semistar operations on Dedekind domains. (English) Zbl 1321.13009 Commun. Algebra 43, No. 1, 236-248 (2015). 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 \(|\mathrm{SStar}(D)|=2^{2^{|\mathrm{Max}(D)|}}\). Reviewer: A. Mimouni (Dhahran) Cited in 3 Documents MSC: 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations Keywords:Dedekind domain; Moore family; principal ideal domain; Semistar operation PDF BibTeX XML Cite \textit{J. Elliott}, Commun. Algebra 43, No. 1, 236--248 (2015; Zbl 1321.13009) Full Text: DOI arXiv Link OpenURL References: [1] Alekseev V. B., Diskretnaya Matematika 1 (2) pp 129– (1989) [2] DOI: 10.1007/978-3-642-11928-6_6 · Zbl 1274.05013 [3] DOI: 10.1016/S0012-365X(97)00099-X · Zbl 0910.06004 [4] DOI: 10.1016/S0021-8693(03)00462-9 · Zbl 1040.13002 [5] DOI: 10.1007/978-3-642-94181-8 [6] Matsuda R., Commutative Semigroup Rings., 2. ed. (2006) [7] DOI: 10.1080/00927870008826974 · Zbl 0964.13006 [8] DOI: 10.1016/j.jpaa.2004.12.019 · Zbl 1088.13008 [9] DOI: 10.1017/S0305004100065403 · Zbl 0658.06007 [10] Okabe A., Math. J. Toyama Univ. 17 pp 1– (1994) [11] DOI: 10.1081/AGB-200063359 · Zbl 1088.13001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.