TW-domains and Strong Mori domains

In this paper we are mainly concerned with TW-domains, i.e., domains in which the w- and t-operations coincide. Precisely, we investigate possible connections with related well-known classes. We characterize the TW-property in terms of divisoriality for Mori domains and Noetherian domains. Specifically, we prove that a Mori domain R is a TW-domain if and only if RM is a divisorial domain for each t-maximal ideal M of R. It turns out that a Mori domain which is a TW-domain is a Strong Mori domain. The last section examines the transfer of the “TW-domain” and “Strong Mori” properties to pullbacks, in order to provide some original examples.