Integral Domains Whose ω-Integral Closures Are Krull Domains  

作　　者：Gyu Whan Chang HwanKoo Kim 

机构地区：[1]Department of Mathematics Education,Incheon National University Incheon 22012,Korea [2]Division of Computer and Information Engineering,Hoseo University Asan 31499,Korea

出　　处：《Algebra Colloquium》2020年第2期287-298,共12页代数集刊（英文版）

基　　金：supported by the Academic Research Fund of Hoseo University in 2017(no.2017-0047).

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 ω-integral closure of D in K;so D ■ 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 ■ D ■ D^[w],t-dim(D)=1,D is a Priifer multiplication domain with v-dim(D)=2,and D^[w] is a UFD.

关 键 词：Krull domain ω-integral closure PVMD t-Nagata ring weakly Dedekind domain 

分 类 号：O15[理学—数学]