Auslander-Buchsbaum定理的推广(英文)  

A Generalization of Auslander-Buchsbaum Theorem

作　　者：唐高华[1] 殷晓斌[2] 佟文廷[3] 

机构地区：[1]广西师范学院数学与计算机科学系,广西南宁530001 [2]安徽师范大学数学系,安徽芜湖241000 [3]南京大学数学系,江苏南京210093

出　　处：《广西科学》2005年第2期97-101,共5页Guangxi Sciences

基　　金：SupportedbyGuangxiNaturalSciencesFoundation(0221029)and theSupportProgramfor100YoungandMiddle-agedDiscipliary LeadersinGuangxiHigherEducationInstitutionsandScientific ReserchFoundationofGuangxiEducationalDepartment.

摘　　要：Auslander-Buchsbaum定理指出,如果R是一个整体维数有限的Noether局部环,M是一个有限生成的非零R-模,那么pdRM+CodimRM=gl.dimR.文献[2]证明上述公式对极大理想为有限生成的凝聚环上的有限表现的非零Noether模依然成立.本文试图将Auslander-Buchsbaum公式推广到任意的交换凝聚环上.The Auslander-Buchsbaum Theorem states that pd_RM+Codim_RM=gl.dimR for each finitely generated nonzero module M over a Noetherian local ring R with finite global dimension.This theorem was generalized to nonzero finitely presented Noetherian modules M over a coherent local ring R with finitely generated maximal ideal J and finite weak global dimension().Our aim is to extend the Auslander-Buchsbaum Theorem to any commutative coherent rings.

关 键 词：凝聚环 有限表现 整体维数 弱整体维数 

分 类 号：O153.3[理学—数学]