形式三角矩阵环上的Gorenstein FP_n- 投射模

Gorenstein FP_n-Projective Module overFormal Triangular Matrix Rings

摘要: 设 T =(_{U B}^{A 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,U_A是平坦模,_BU 是有限生成投射模, M =(_{M 2} ^{M ₁} ) _φ^M 是左 T-模,若 M₁ 是Gorenstein FP_n 投射左A-模, M₂/Imφ^M 是 Gorenstein FP_n- 投射左 B-模,且 ϕ^M 是单同态,则 M 是 Gorenstein FP_n-投射左 T -模. 进而: U ⊗_A M₁ 是 Gorenstein FP_n- 投射左 B-模,当且仅当, M₂ 是 Gorenstein FP_n- 投射左 B-模.

Abstract: Let T =(_{U B}^{A 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, U_A is a at module, _BU is a finitely generated projective module, M =(_{M 2} ^{M ₁} ) _φ^M is a left T-module. If M₁ is a Gorenstein FP_n-projective left A-module, M₂/Imφ^M is a Gorenstein FP_n-projective left B-module and ϕ^M is injective. Then M is a Gorenstein FP_n-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.