Locally Self-Injective Property of FI^(m)  

作　　者：Duo Zeng 

机构地区：[1]LCSM(Ministry of Education),School of Mathematics and Statistics Hunan Normal University,Changsha 410081,China

出　　处：《Algebra Colloquium》2024年第1期97-110,共14页代数集刊（英文版）

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

摘　　要：We consider the locally self-injective property of the product FI^(m) of category FI of finite sets and injections.Explicitly,we prove that the external tensor product commutes with the coinduction functor,and hence preserves injective modules.As 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.

关 键 词：self-injective property Serre quotient FI^(m)-modules 

分 类 号：O15[理学—数学]