摘要:
设A、B是环,M是B-A-双模,称T=(A 0 M B)是形式三角矩阵环.设R是任何环,N是R-模,若对R的任意伪凝聚模M,有Ext1R(M,N)=0,则称N是PC-内射模.借助有限表现模的性质刻画形式三角矩阵环的凝聚性,证明若M是有限表现右A-模,则T是右凝聚环当且仅当A和B都是右凝聚环.讨论形式三角矩阵环上的模的性质,证明若T是右凝聚环,M是有限表现右A-模,则有右T-模(X,Y)f是PC-内射模当且仅当X是PC-内射A-模,ker(f)是PC-内射B-模,且(f)是满同态.%Let A,B be rings,M be a B-A-biamodule,T be the formal triangular ring ( A 0 M B) . Let R be a ring,and N be an R-module. If Ext 1R (M,N)=0 for any pseudo-coherent R-module M,then N is called a PC-injective module. Based on the finite present properties of modules,in this paper we investigate the coherence of formal triangular rings. Let M be the right finite present A-module. We prove that T is right coherent if and only if both A and B are right coherent. Assume that T is right coherent and M is right finite present A-module. We prove that right T-module (X,Y)f is PC-injective if and only if X is PC-injective A-module,ker (f) is PC-injective B-module and (f) is surjective.