关于强FP n-内射模  

On strongly FP n-injective modules

作　　者：陈东 胡葵[2] 陈明钊 CHEN Dong;HU Kui;CHEN Ming-zhao(College of Information Science and Engineering,Chengdu University,Chengdu 610106,Sichuan,China;College of Science,Southwest University of Science and Technology,Mianyang 621010,Sichuan,China;School of Mathematics and Information Science,Leshan Normal College,Leshan 614000,Sichuan,China)

机构地区：[1]成都大学信息科学与工程学院,四川成都610106 [2]西南科技大学理学院,四川绵阳621010 [3]乐山师范学院数学与信息科学学院,四川乐山614000

出　　处：《西北师范大学学报（自然科学版）》2020年第5期36-41,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11671283);四川省教育厅科研基金资助项目(18ZB0138);成都大学校青年基金资助项目(2018XZA08)。

摘　　要：通过引入强FP n-内射模和强FP n-平坦模的概念,证明了环R是n-凝聚环当且仅当强FP n-内射模关于正向极限封闭,环R是n-遗传环当且仅当强FP n-内射模的商模是强FP n-内射模;讨论了每个R-模是强FP n-内射模的环类,证明了R是n-Von Neumann正则环当且仅当每个R-模是强FP n-内射模.The concepts of strongly FP n-injective modules and strongly FP n-flat modules are introduced,it is proved that a ring R is n-coherent ring if and only if strongly FP n-injective module is closed under direct limit,and a ring R is n-hereditary if and only if the quotient module of strongly FP n-injective module is strongly FP n-injective.The rings over which every R-module is a strongly FP n-injective is discussed,it is proved that a ring R is a n-Von Neumann regular if and only if every R-module is a strongly FP n-injective.

关 键 词：强FP n-内射模 n-凝聚环 n-遗传环 n-Von Neumann正则环 商模 

分 类 号：O154[理学—数学]