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 ∈ S and a princip...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 ∈ S and a principal ideal （c） of D such that sI （c） 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.展开更多
文摘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 ∈ S and a principal ideal （c） of D such that sI （c） 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.
