A NOTE ON (*w)-NOETHERIAN DOMAINS

作者：Hwang Chul Ju^*; Lim Jung Wook

来源：Proceedings of the American Mathematical Society, 2013, 141(4): 1199-1209.

• (*w)-operation
• (*w)-Noetherian domain

Let D be an integral domain with quotient field K, * be a star-operation on D, and GV *(D) be the set of finitely generated ideals J of D such that J* = D. Then the map *(w) defined by I-*w = {x is an element of K vertical bar Jx subset of I for some J is an element of GV *(D)} for all nonzero fractional ideals I of D is a finite character star-operation on D. In this paper, we study several properties of (*w)-Noetherian domains. In particular, we prove the Hilbert basis theorem for (*w)-Noetherian domains.

• 出版日期2013-4