分次单内射模及其刻画  

Graded Simple Injective Modules and Their Characterization

作　　者：梁春梅 王芳贵[1] 吴小英[1] LIANG Chunmei;WANG Fanggui;WU Xiaoying(College of Mathematics and Software Science,Sichuan Normal University,Chengdu Sichuan 610068,China)

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610068

出　　处：《广西师范大学学报（自然科学版）》2019年第2期113-120,共8页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11671283)

摘　　要：本文引入了分次单内射模的概念。设R是分次环,分次R-模N称为分次单内射模,是指对任何分次单R-模S,有EXT1R(S,N)=0。也给出了分次单内射模的系列等价刻画,证明了若R是左分次Artin环,或R是分次Krull维数不超过1的分次Noether环,则分次模E是分次内射模当且仅当E是分次单内射模。In this paper,the concept of graded simple injective modules is introduced.Let R be a G-graded ring.A graded R-module N is called a graded single injective module if EXT 1 R(S,N)=0 for any graded simple R-module S.A series of equivalent characterizations for graded simple injective modules are given,and it is shown that:if R is a left graded Artinian ring or R is a graded Noetherian ring with the graded Krull dimension at most one,then a graded module E is graded injective if and only if E is graded simple injective.

关 键 词：分次环 分次单模 分次内射模 分次单内射模 分次Noether环 

分 类 号：O153.3[理学—数学] O154[理学—基础数学]