(n,m)-强投射余可解Gorenstein平坦模

(n,m)-Strongly projectively coresolved Gorenstein flat modules

引入(n,m)-强投射余可解Gorenstein平坦模(即(n,m)-强PGF模)的概念,给出它的一些基本性质。证明了如果M是一个(n,m)-强PGF模,则:(1)M的PGF维数PGFd(M)≤m;(2)当1≤i≤m时,M的第i个合冲是(n,m-i)-强PGF模;当i≥m时,M的第i个合冲是(n,0)-强PGF模。其次证明了:如果模M的第d个合冲是(1,m)-强PGF模,则PGFd(M)=k≤d+m,且M是(1,k)-强PGF模。

The concept of an(n,m)-strongly projectively coresolved Gorenstein flat module(i.e.(n,m)-strongly PGF module)is introduced,and some basic properties of it are given.It is proved that if M is an(n,m)-strongly PGF module,then(1)PGF dimension of M PGFd(M)≤m;(2)when 1≤i≤m,the ith syzygy of M is(n,m-i)-strongly PGF module;when i≥m,the ith syzygy of M is(n,0)-strongly PGF module.Secondly,it is proved that the dth syzygy of M is(1,m)-strongly PGF module,then PGF d(M)=k≤d+m,and M is(1,k)-strongly PGF module.