形式三角矩阵环上的Gorenstein FP-内射维数
Gorenstein FP-injective dimensions over formal triangular matrix rings
张翠萍 1董娇娇 1杨银银1
作者信息
- 1. 西北师范大学数学与统计学院,甘肃兰州 730070
- 折叠
摘要
设T=(A 0 U B)是形式三角矩阵环其中A、B是环U是(B,A)双模M=(M1M2)φM是左T-模.证明若T是左GFPI封闭的左凝聚环,UA是平坦的,BU是有限表示的且pd(BU)＜∞,则以下式子成立:(1)max { G-FP-id(M1),G-FP-id(M2)} ≤G-FP-id(M);(2)G-FP-id(M)≤max {G-FP-id(M1),G-FP-id(M2)+1};(3)max{ lG-FP-id(A),lG-FP-id(B){ ≤lG-FP-id(T)≤max{ lG-FP-id(A),lG-FP-id(B)+1}.
Abstract
Let T=(A 0 U B)be a formal triangular matrix ring,where A and B are rings and U is a(B,A)-bimodule.Let M=(M12M)φM be a left T-module.The results are proved that if T is a left GFPI-closed and left coherent ring,UA is flat,BU is finitely presented and pd(BU)＜∞,then:(1)max{ G-FP-id(M1),G-FP-id(M2)}≤ G-FP-id(M);(2)G-FP-id(M)≤max { G-FP-id(M,),G-FP-id(M2)+1 };(3)max { lG-FP-id(A),lG-FP-id(B)}≤ lG-FP-id(T)≤max { lG-FP-id(A),lG-FP-id(B)+1 }.
关键词
形式三角矩阵环/Gorenstein/FP-内射模/Gorenstein/FP-内射维数Key words
formal triangular matrix ring/Gorenstein FP-injective module/Gorenstein FP-injective dimension引用本文复制引用
出版年
2024
NETL
NSTL
万方数据