Integral Domains Whose w-Integral Closures Are Krull Domains

• 作者: Gyu Whan Chang HwanKoo Kim
• 来源期刊: 代数集刊（英文版）
• 关键词: Krull domain w-integral closure PvMD t-Nagata ring weakly Dedekind domain
• 年，卷（期）: 2020,（2）
• 页码范围: 287-298
• 页数: 12页
• 语种: 英文
• DOI: 10.1142/S1005386720000231

摘要

Let D be an integral domain with quotient field K,(D) be the integral closure of D in K,and D[w]be the w-integral closure of D in K;so (D) (C) D[w],and equality holds when D is Noetherian or dim(D) =1.The Mori-Nagata theorem states that if D is Noetherian,then (D) is a Krull domain;it has also been investigated when (D) is a Dedekind domain.We study integral domains D such that D[w]is a Krull domain.We also provide an example of an integral domain D such that D (C)(D) (C) D[w],t-dim(D) =1,(D) is a Prüfer v-multiplication domain with t-dim((D)) =2,and D[w]is a UFD.