Two Notes on Automorphisms of Modules over a PID

• 来源期刊: 代数集刊（英文版）
• 关键词: automorphism of modules finitely generated module module with minimum condition on submodules
• 年，卷（期）: 2019,（3）
• 页码范围: 401-410
• 页数: 10页
• 语种: 英文
• DOI: 10.1142/S1005386719000294

摘要

Let D 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 x,y are two elements in M such that M/Dx≌ M/Dy,then there exists an automorphism α of M such that α(x) =y.(ii) If M satisfies the minimal condition 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 α of M such that α(X) =Y.