形式三角矩阵环上的Gorenstein FP-内射维数  

Gorenstein FP-injective dimensions over formal triangular matrix rings

作　　者：张翠萍 董娇娇 杨银银 ZHANG Cuiping;DONG Jiaojiao;YANG Yinyin(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2024年第2期8-13,共6页Journal of Shandong University(Natural Science)

摘　　要：设■是形式三角矩阵环,其中A、B是环,U是(B,A)-双模,■是左T-模。证明若T是左GFPI封闭的左凝聚环,U_(A)是平坦的,_(B)U是有限表示的且pd(_(B)U)<∞,则以下式子成立:(1) max{G-FP-id(M_(1)), G-FP-id(M_(2))}≤G-FP-id(M);(2) G-FP-id(M)≤max{G-FP-id(M_(1)), G-FP-id(M_(2))+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}。Let T=■be a formal triangular matrix ring,where A and B are rings and U is a(B,A)-bimodule.Let M=■be a left T-module.The results are proved that if T is a left GFPI-closed and left coherent ring,U_(A) is flat,_(B)U is finitely presented and pd(_(B)U)<∞,then:(1)max{G-FP-id(M_(1)),G-FP-id(M_(2))}≤G-FP-id(M);(2)G-FP-id(M)≤max{G-FP-id(M_(1)),G-FP-id(M_(2))+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 

分 类 号：O153.3[理学—数学]