Let D be a finite-dimensional integral domain, Spec（D） be the set of prime ideals of D, and SpSS（D） be the set of spectral semistar operations on D. Mimouni gave a complete description for the prime ideal structur...Let D be a finite-dimensional integral domain, Spec（D） be the set of prime ideals of D, and SpSS（D） be the set of spectral semistar operations on D. Mimouni gave a complete description for the prime ideal structure of D with ｜SpSS（D）｜ = n ＋ dim（D） for 1 ≤ n ≤5 except for the quasi-local cases of n = 4, 5. In this paper, we show that there is an integral domain D such that ｜SpSS（D） ｜ = n＋dim（D） for all positive integers n with n ≠ 2. As corollaries, we completely characterize the quasi-local domains D with ｜SpSS（D）｜= n＋dim（D） for n = 4, 5. Furthermore, we also present the lower and upper bounds of ISpSS（D）I when Spee（D） is a finite tree.展开更多
文摘Let D be a finite-dimensional integral domain, Spec（D） be the set of prime ideals of D, and SpSS（D） be the set of spectral semistar operations on D. Mimouni gave a complete description for the prime ideal structure of D with ｜SpSS（D）｜ = n ＋ dim（D） for 1 ≤ n ≤5 except for the quasi-local cases of n = 4, 5. In this paper, we show that there is an integral domain D such that ｜SpSS（D） ｜ = n＋dim（D） for all positive integers n with n ≠ 2. As corollaries, we completely characterize the quasi-local domains D with ｜SpSS（D）｜= n＋dim（D） for n = 4, 5. Furthermore, we also present the lower and upper bounds of ISpSS（D）I when Spee（D） is a finite tree.
