Linkage of ideals under star operations

Linkage classically characterizes several fundamental classes of domains: a Noetherian domain is Dedekind if and only if it has the primary linkage property; a domain is almost Dedekind (resp., Prüfer) if and only if it has the linkage (resp., finite linkage) property; and a finite-dimensional valuation domain is a DVR if and only if it has the primary linkage property. Motivated by these characterizations, this paper develops a unified framework for linkage of ideals via star operations, recovering the theory in the trivial operation case and producing sharp analogues of the classical picture. We prove that a domain is a v-domain if and only if it has the finite t-linkage property; it is completely integrally closed if and only if it has the v-linkage property; it is a PvMD if and only if it has the finite w-linkage property; and it is t-almost Dedekind if and only if it has the w-linkage property.