n-余纯Gorenstein AC模

n-copure Gorenstein AC modules

设R是环,n是固定非负整数,GJ_(n)(GF_(n))是Gorenstein AC内射(Gorenstein AC平坦)维数至多为n的左(右)R-模构成的类。称左(右)R-模M是n-余纯Gorenstein AC-内射模(n-余纯Gorenstein AC平坦模),若对任意的N∈GJ_(n),都有Ext_(R)^(1)(N,M)=0(Tor_(1)^(R)(M,N)=0)。证明了有限表现右R-模M是n-余纯Gorenstein AC平坦的当且仅当M是右R-模K的GF_(n)-预包络K→F的上核,其中F是平坦的。

Let R be a ring,n a fixed nonnegative integer andGJ_(n)(resp.,GF_(n))the class of all left(resp.,right)R-modules of Gorenstein AC injective(resp.,Gorenstein AC flat)dimension at most n.A left R-module M(resp.,right R-module M)is called n-copure Gorenstein AC injective(resp.,n-copure Gorenstein AC flat)if Ext_(R)^(1)(N,M)=0(resp.,Tor_(1)^(R)(M,N)=0)for any N∈G In.It is proven that a finitely presented right R-module M is n-copure Gorenstein AC flat if and only if M is a cokernel of a GFnpreenvelope K→F of a right R-module K with F flat.