Two Notes on Auto morphisms of Modules over a PID  

作　　者：Heguo Liu Xiaoliang Luo Xin Qin Bomin Zan 

机构地区：[1]School of Mathematics and Statistics,Hubei University,Wuhan 430062,China

出　　处：《Algebra Colloquium》2019年第3期401-410,共10页代数集刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11771129).

摘　　要：Let Z>be a principal ideal domain(PID)and M be a module over D.We prove the following two dual results:(i)If M is finitely generated and rr,y are two elements in M such that M/Dx≌M/Dy,then there exists an auto morphism a of M such that a(x)=y.(ii)If M satisfies the minimal cond计ion on submodules and X,Y are two locally cyclic submodules of M such that M/X≌M/Y and X≌Y,then there exists an automorphism a of M such that α(X)=Y.

关 键 词：AUTO MORPHISM of MODULES finitely generated MODULE MODULE with minimumcondition on submodules 

分 类 号：O15[理学—数学]