THE t#-PROPERTY FOR INTEGRAL DOMAINS

M∈M2 RM whenever M1 and M2 are distinct subsets of the set of maximal ideals of R. Prüfer domains satisfying the #-condition were first studied in [9] and [10]. Domains each of whose overrings satisfy the #-condition were also studied in [10] (in the Prüfer case); these domains have come to be called ##-domains. Although the papers mentioned above contain very interesting results, those results are essentially restricted to the class of Prüfer domains. This paper represents an effort to extend, by a modification of the definitions, results about the #and ##-conditions to a much wider class of domains. In the first section, we introduce the t#-condition: A domain R satisfies the t#-condition if ⋂