Two Notes on Auto morphisms of Modules over a PID

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.