S-*w-Principal Ideal Domains

Let D be an integral domain, * a star-operation on D, and S a multiplicative subset of D. We define D to be an S-*(w)-principal ideal domain if for each nonzero ideal I of D, there exist an element s is an element of S and a principal ideal (c) of D such that sI subset of (c) subset of I-*w. In this paper, we study some properties of S-*(w) -principal ideal domains. Among other things, we study the local property, the Nagata type theorem, and the Cohen type theorem for S-*(w)-principal ideal domains.