GENERALLY t-LINKATIVE DOMAINS

Abstract

An overring t of an integral domain R is t-linked over R if for each finitely generated nonzero ideal I of R, (T : IT) ⊋ T implies (R : I) ⊋ R. A t-linkative domain is one for which each overring is t-linked. The notion of a generally t-linkative domain is introduced as a domain R such that [Formula: see text] is t-linkative for each finite type system of ideals [Formula: see text]. In general, R is generally t-linkative if and only if RM is generally t-linkative for each maximal ideal M. All Prüfer domains are generally t-linkative as are all one-dimensional domains and all pseudo-valuation domains. If R is Noetherian and not a field, then it is generally t-linkative if and only if it is one-dimensional. In contrast, an example is given of a two-dimensional Mori domain that is generally t-linkative.