V_c-Noetherian domains and Krull domains

Abstract

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.