Locally Self-Injective Property of FI^(m)

作     者：Duo Zeng 

作者机构：LCSM(Ministry of Education)School of Mathematics and Statistics Hunan Normal UniversityChangsha 410081China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2024年第31卷第1期

页      面：97-110页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：partially supported by the National Natural Science Foundation of China(11771135) 

主　　题：self-injective property Serre quotient FI^(m)-modules 

摘      要：We consider the locally self-injective property of the product FI^(m) of category FI of finite sets and ***,we prove that the external tensor product commutes with the coinduction functor,and hence preserves injective *** corollaries,every projective FI^(m)-module over a field of characteristic O is injective,and the Serre quotient of the category of finitely generated FI^(m)-modules by the category of finitely generated torsion FI^(m)-modules is equivalent to the category of finite-dimensional FI^(m)-modules.