Let D be an integrally closed domain, \(\{V_{\alpha }\}\) be the set of t-linked valuation overrings of D, and \(v_c\) be the star operation on D defined by \(I^{v_c} = \bigcap _{\alpha } IV_{\alpha }\) for all nonzero fractional ideals I of D. In this paper, among other things, we prove that D is a \(v_c\)-Noetherian domain if and only if D is a Krull domain, if and only if \(v_c = v\) and every prime t-ideal of D is a maximal t-ideal. As a corollary, we have that if D is one-dimensional, then \(v_c = v\) if and only if D is a Dedekind domain.

中文翻译：

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$$ v_c $$ vc -Noetherian域和Krull域

设D为一个整体封闭域，\（\ {V _ {\ alpha} \} \）为D的t链接估值环的集合，而\（v_c \）为D由\（I ^ {} V_C = \ bigcap _ {\阿尔法} IV _ {\阿尔法} \）对于所有非零分式理想我的d。在本文中，除其他外，我们证明D是\（ v_c \）- Noetherian域，当且仅当D是Krull域，并且当且仅当\（v_c = v \）并且每个素数t理想D是最大t-理想的。推论是，如果D是一维的，则当且仅当D是Dedekind域时，\（v_c = v \）。