Some Results on Noetherian Warfield Domains  

作　　者：Kui Hu Jung Wook Lim Dechuan Zhou 

机构地区：[1]College of Science,Southwest University of Science and Technology Mianyang,Sichuan 621010,China [2]Kyungpook National University,Daegu 41566,Korea [3]Department of Mathematics,College of Natural Sciences Kyungpook National University,Daegu 41566,Korea

出　　处：《Algebra Colloquium》2022年第1期67-78,共12页代数集刊（英文版）

基　　金：This work was partially supported by the Department of Mathematics in Kyungpook National University and National Natural Science Foundation of China(Grant No.11671283);The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(2017R1C1B1008085),Korea.

摘　　要：Let R be a domain.In this paper,we show that if R is one dimensional,then R is a Noetherian Warfield domain if and only if every maximal ideal of R is 2-generated and for every maximal ideal M of R,M is divisorial in the ring(M:M).We also prove that a Noetherian domain R is a Noetherian Warfield domain if and only if for every maximal ideal M of R,M^(2) can be generated by two elements.Finally,we give a sufficient condition under which all ideals of R are strongly Gorenstein projective.

关 键 词：strongly Gorenstein projective module Noetherian Warfield domain strongly Gorenstein Dedekind domain 

分 类 号：O15[理学—数学]