形式三角矩阵环上的F-Gorenstein平坦模

F-Gorenstein Flat Modules over Formal Triangular Matrix Rings

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.利用Hom函子和伴随同构等理论,刻画形式三角矩阵环T上的F-Gorenstein平坦模结构,并证明若BU的平坦维数有限,U A的平坦维数有限且对任意的余挠左A-模C,有U■AC是余挠左B-模,则左T-模M_(1)/M_(2)φ^(M)是F-Gorenstein平坦模当且仅当M_(1)是F-Gorenstein平坦左A-模,Cokerφ^(M)是F-Gorenstein平坦左B-模,且φ^(M):U■AM 1→M_(2)是单射.

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.Using Hom functors and adjoint isomorphism theory,we describe the structure of the F-Gorenstein flat modules over formal triangular matrix ring T and prove that if BU has finite flat dimension,U A has finite flat dimension and U■AC is a cotorsion left B-module for any cotorsion left A-module C,then a left T-module M_(1) M_(2)φ^(M) is F-Gorenstein flat if and only if M_(1) is F-Gorenstein flat left A-module,Cokerφ^(M) is F-Gorenstein flat left B-module,andφ^(M):U■AM 1→M_(2) is a monomorphism.