摘要
设R是含幺交换环,X■SpecR,E是R模,M是E的子模,对任意子模N≤E,若满足Supp(M∩N)■X,必有SuppN■X,则称E是M相对于X的本性扩张,记为M⊿/XE.本文给出相对本性扩张的两个等价条件.若R是Noether环,则M⊿/XE当且仅当Mp■Ep,p∈SpecR-X;若X是饱和素理想集合,则还有等价条件HomeRp(k(p),Mp)=HomeRp(k(p),Ep),p∈SpecR-X.此外,本文还给出了相对本性扩张的一些性质.
Let R be a commutative ring with unit element,X lohtain in SpecR, E a R-module and submodule M≤ E, if for any submodule N≤ E, Suppn （M∩N） C X implies SuppN lohtain in X,then we say E is an essential extension of M with respect to X, abbreviated M△/xE. In this paper, We give two equivalent statements of relative essential extension. Let R be a commutative Noetherian ring, then M△/xE if and only if Mp △Ep, A p ∈SpecR -X;if X be a saturated set of prime ideals, then we also have another equivalent condition HomRp （ k （p）, Mp ） = HOmRp （ k （p）, Ep ）, A p e SpeeR - x. In addition,we also present some properties of relative essential extension.
出处
《苏州大学学报（自然科学版）》
CAS
2008年第4期28-32,共5页
Journal of Soochow University(Natural Science Edition)
关键词
本性扩张
相对本性扩张
Bass数
essential extension
relative essential extension
Bass number
