The Auslander-type condition of triangular matrix rings  

作　　者：HUANG ChongHui HUANG ZhaoYong 

机构地区：[1]School of Mathematics and Physics, University of South China, Hengyang 421001, China [2]Department of Mathematics, Nanjing University, Nanjing 210093, China

出　　处：《Science China Mathematics》2012年第8期1647-1654,共8页中国科学：数学（英文版）

基　　金：supported by the Specialized Research Fund for the Doctoral Pro-gram of Higher Education(Grant No.20100091110034);National Natural Science Foundation of China(Grant Nos.11171142,11126169,11101217);Natural Science Foundation of Jiangsu Province of China(Grant Nos.BK2010047,BK2010007);the Scientific Research Fund of Hunan Provincial Education Department(Grant No.10C1143);a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions

摘　　要：Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to satisfy the Auslander-type condition Gn（k） if the right fiat dimension of the （i ＋ 1）-th term in a minimal injective resolution of RR is at most i ＋ k for any 0 ≤ i ≤ n - 1. In this paper, we prove that R is Gn（k） if and only if so is a lower triangular matrix ring of any degree t over R.Let R be a left and right Noetherian ring and n,k be any non-negative integers.R is said to satisfy the Auslander-type condition G n (k) if the right flat dimension of the (i + 1)-th term in a minimal injective resolution of RR is at most i + k for any 0 i n 1.In this paper,we prove that R is Gn (k) if and only if so is a lower triangular matrix ring of any degree t over R.

关 键 词：Auslander-type condition triangular matrix rings  fiat dimension  minimal injective resolutions mlnlm^l A.t r^nlllti^n~ 

分 类 号：O153.3[理学—数学] TM402[理学—基础数学]