设 T =(U BA 0)是形式三角矩阵环, 其中 A, B 是环, U 是 (B, A)-双模. 证明了当 T 是左n-凝聚环,UA是平坦模,BU 是有限生成投射模, M =(M 2 M 1 ) φM 是左 T-模,若 M1 是Gorenstein FPn 投射左A-模, M2/ImφM 是 Gorenstein FPn- 投射...设 T =(U BA 0)是形式三角矩阵环, 其中 A, B 是环, U 是 (B, A)-双模. 证明了当 T 是左n-凝聚环,UA是平坦模,BU 是有限生成投射模, M =(M 2 M 1 ) φM 是左 T-模,若 M1 是Gorenstein FPn 投射左A-模, M2/ImφM 是 Gorenstein FPn- 投射左 B-模,且 ϕM 是单同态,则 M 是 Gorenstein FPn-投射左 T -模. 进而: U ⊗A M1 是 Gorenstein FPn- 投射左 B-模,当且仅当, M2 是 Gorenstein FPn- 投射左 B-模.Let T =(U BA 0) be a formal triangular matrix ring, where A and B are rings and U is (B;A)-bimodule. It is proved that T is a left n-cocherent ring, UA is a at module, BU is a finitely generated projective module, M =(M 2 M 1 ) φM is a left T-module. If M1 is a Gorenstein FPn-projective left A-module, M2/ImφM is a Gorenstein FPn-projective left B-module and ϕM is injective. Then M is a Gorenstein FPn-projective left T-module. In this instance, U ⊗A M1 is a Gorenstein FPn-projective left B-module, if and only if, M2 is a Gorenstein FPn-projective left B-module.展开更多
Du Xianneng和Chen Zhengxin用Gorenstein内射模刻画了Gorenstein环.作者根据Gorenstein投射模来刻画Gorenstein环,利用推出图,得到了定理3.由该文可以看出n-Gorenstein环与Gorenstein投射模的对应关系.在此基础上,又得到了定理4中的两...Du Xianneng和Chen Zhengxin用Gorenstein内射模刻画了Gorenstein环.作者根据Gorenstein投射模来刻画Gorenstein环,利用推出图,得到了定理3.由该文可以看出n-Gorenstein环与Gorenstein投射模的对应关系.在此基础上,又得到了定理4中的两个结论的等价性,在一定意义上拓展了Gorenstein投射模的有关结论.展开更多
文摘设 T =(U BA 0)是形式三角矩阵环, 其中 A, B 是环, U 是 (B, A)-双模. 证明了当 T 是左n-凝聚环,UA是平坦模,BU 是有限生成投射模, M =(M 2 M 1 ) φM 是左 T-模,若 M1 是Gorenstein FPn 投射左A-模, M2/ImφM 是 Gorenstein FPn- 投射左 B-模,且 ϕM 是单同态,则 M 是 Gorenstein FPn-投射左 T -模. 进而: U ⊗A M1 是 Gorenstein FPn- 投射左 B-模,当且仅当, M2 是 Gorenstein FPn- 投射左 B-模.Let T =(U BA 0) be a formal triangular matrix ring, where A and B are rings and U is (B;A)-bimodule. It is proved that T is a left n-cocherent ring, UA is a at module, BU is a finitely generated projective module, M =(M 2 M 1 ) φM is a left T-module. If M1 is a Gorenstein FPn-projective left A-module, M2/ImφM is a Gorenstein FPn-projective left B-module and ϕM is injective. Then M is a Gorenstein FPn-projective left T-module. In this instance, U ⊗A M1 is a Gorenstein FPn-projective left B-module, if and only if, M2 is a Gorenstein FPn-projective left B-module.
