| 引用本文： |
-
唐高华,殷晓斌,佟文廷.Auslander-Buchsbaum定理的推广[J].广西科学,2005,12(2):97-101. [点击复制]
- Tang Gaohua,Yin Xiaobin,Tong Wenting.A Generalization of Auslander-Buchsbaum Theorem[J].Guangxi Sciences,2005,12(2):97-101. [点击复制]
|
|
| 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. |
| 关键词: 凝聚环 有限表现 整体维数 弱整体维数 |
| DOI： |
| 投稿时间：2004-08-17 |
| 基金项目:Supported by Guangxi Natural Sciences Foundation (0221029) and the Support Program for 100 Young and Middle-aged Discipliary Leaders in Guangxi Higher Education Institutions and Scientific Reserch Foundation of Guangxi Educational Department. |
|
| A Generalization of Auslander-Buchsbaum Theorem |
|
Tang Gaohua1, Yin Xiaobin2, Tong Wenting3
|
| (1.Dept. of Math. & Comp. Sci., Guangxi Teachers Education Coll., Nanning, Guangxi, 530001, China;2.Dept. of Math., Anhui Normal Univ., Wuhu, Anhui, 241000, China;3.Dept. of Math., Nanjing Univ., Nanjing, Jiangsu, 210093, China) |
| Abstract: |
| The Auslander-Buchsbaum Theorem states that pdRM+CodimRM=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([2]).Our aim is to extend the Auslander-Buchsbaum Theorem to any commutative coherent rings. |
| Key words: coherent ring finitely presented global dimension weak global dimension |
