Nagata-like theorems for integral domains of finite character and finite t-character

Abstract

An integral domain D is said to be of finite character (resp., finite t-character) if every nonzero nonunit of D belongs to at most a finite number of maximal ideals (resp., maximal t-ideals) of D. Let S be a multiplicative set of D. In this paper we study when DSbeing of finite character (resp., finite t-character) implies that D is of finite character (resp., finite t-character).