关于局部Noether模(英文)

On Locally Noetherian Modules

英文关键词:locally noetherian module  finitely cogenerated module  X-modu

中文摘要:

      本文证明了如下结果：左 Ｒ－模 Ｍ是局部 Ｎｏｅｔｈｅｒ模当且仅当σ［Ｍ］中的任意Ｍ－内射左Ｒ－模的直和是一个有限余生成左Ｒ－模和一个拟连续（或连续，直内射）左Ｒ－模的直和．

英文摘要:

      This paper is devoted to give some characterizations of locally noetherian modules by finitely cogenerated modules and generalized injective modules. It is proved that a left R-module M is locally noetherian if and only if every direct sum of M-injective left R-modules in σ[M] is the direct sum of a finitely cogenerated left R-module and a quasi-continuous (or, continuous, or, direct-injective, etc,) left R-module.