浙江大学学报（理学版）
浙江大學學報（理學版）
절강대학학보（이학판）
JOURNAL OF ZHEJIANG UNIVERSITY
2010年
2期
123-125,147
,共4页
纯理想%余挠模%PI-内射模%Noether环%von Neumann正则环%完全环%弱完全环
純理想%餘撓模%PI-內射模%Noether環%von Neumann正則環%完全環%弱完全環
순이상%여뇨모%PI-내사모%Noether배%von Neumann정칙배%완전배%약완전배
pure ideal%cotorsion module%PI-injeetive module%Noetherian ring%von Neumann regular ring%perfect ring%weakly perfect ring
引入PI-内射模,它是余挠模的一种自然推广.通过对PI-内射模的研究,定义了弱完全环并给出了Noether环与won Neumann正则环的一些新刻画.证明了:(1)若R为右Noether环,则每个右R-模都是PI-内射的;(2)Noether环R是完全环当且仅当R上的所有PI-内射模是余挠的.
引入PI-內射模,它是餘撓模的一種自然推廣.通過對PI-內射模的研究,定義瞭弱完全環併給齣瞭Noether環與won Neumann正則環的一些新刻畫.證明瞭:(1)若R為右Noether環,則每箇右R-模都是PI-內射的;(2)Noether環R是完全環噹且僅噹R上的所有PI-內射模是餘撓的.
인입PI-내사모,타시여뇨모적일충자연추엄.통과대PI-내사모적연구,정의료약완전배병급출료Noether배여won Neumann정칙배적일사신각화.증명료:(1)약R위우Noether배,칙매개우R-모도시PI-내사적;(2)Noether배R시완전배당차부당R상적소유PI-내사모시여뇨적.
The notion of PI-injective module is introduced, which is a natural generalization of cotorsion module. By discussing the properties of PI-injective modules, the weakly perfect ring is defined and some new characterizations of yon Neumann regular rings and Noetherian rings are given. The following results are proved: (1) Let R be a ring. If R is right Noetherian, then each right R-module is PI-injective; (2) Let R be a Noetherian ring. Then R is perfect if and only if each PI-injective module is eotorsion.
