w-Noether环上的内射模  

Injectve Modules over w-Noetherian Rings

作　　者：王芳贵[1] 张俊[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610068

出　　处：《数学学报（中文版）》2010年第6期1119-1130,共12页Acta Mathematica Sinica：Chinese Series

基　　金：教育部博士点专项科研基金资助项目(20060636001);四川省重点学科建设基金资助项目(SZD0406)

摘　　要：设R是交换环,如果R满足w-理想的升链条件,则R称为w-Noether环.本文证明了R是w-Noether环当且仅当GV无挠的内射模的直和是内射模,当且仅当每个GV-无挠的内射模是∑-内射模.同时,还证明了在w-Noether环上,每个GV-无挠的内射模都是不可分解的内射模的直和,且每个直和项同构于某个E(R/p),其中p是R的素w-理想,E(R/p)是R/p的内射包.Let R be a commutative ring and let J be a finitely generated ideal of R.J is called a GV-ideal if the natural homomorphism R→Hom_R（J,R） is isomorphic.Let GV（R） be the set of GV-ideals of R.A module M is called GV-torsion-free if Jx=0 with J∈GV（R） and x∈M implies x = 0.A GV-torsion-free module M is called a w-module if Ext_R^1（R/J,M） = 0 for any J∈GV（R）.A ring R is called w-Noetherian if R has if R has the ascending chain condition on w-ideals.In this paper we show that R is a w-Noetherian ringas if and only if every direct sum of GV-torsion-free injective modules is injective;if and only if every GV-torsion-free injective module is∑-injective.Meanwhile,we also prove that every GV-torsion-free injective module over a w-Noetherian ring is a direct sum of indecomposable injective submodules and every indecomposable injective module has the form E（R/p）,where p is a prime w-ideal of R.

关 键 词：有限型模 w-Noether环 ∑-内射模 

分 类 号：O153.3[理学—数学] O154[理学—基础数学]