摘要: 本文研究了形式三角矩阵环上的强Gorenstein FP-内射模。 设
![](https://image.hanspub.org/IMAGE/Edit_34094797-e051-4f8b-94c4-cef737ef3654.png)
是形式三角矩阵环,其中 A 和 B 是环, U 是左 B-右 A-双模。证明了若T 是左凝聚环,
BU 是有限表示的且
![](https://image.hanspub.org/IMAGE/Edit_065ee818-e013-47ba-aef9-88992b1977e5.png)
是强Gorenstein FP-内射左 T -模,则
![](https://image.hanspub.org/IMAGE/Edit_bdf8e662-7c18-4e45-82a4-eafa9c1b6aa5.png)
是强Gorenstein FP-内射左A-模,M
2是强Gorenstein FP-内射左B-模,且
![](https://image.hanspub.org/IMAGE/Edit_ef8663d6-7013-4f13-b073-ac64b25e6664.png)
是满同态。
Abstract:
This paper considers strongly Gorenstein FP-injective modules over formal triangular matrix rings. Let
![](https://image.hanspub.org/IMAGE/Edit_f6abddf3-7aff-499b-bfcd-7f92f90d8d4b.png)
be formal triangular matrix ring, where A and B are two rings and U is a (B;A)-bimodule. It is proved that if T is a left coherent ring,
BU is finitely presented and
![](https://image.hanspub.org/IMAGE/Edit_24ac4913-832d-43f1-a3d4-0fbecc0a0c11.png)
is strongly Gorenstein FP-injective left T-modules, then
![](https://image.hanspub.org/IMAGE/Edit_831b0b3f-f897-4592-9d50-a7d8eb5364e6.png)
is strongly Gorenstein FP-injective left A-modules, M
2 is strongly Gorenstein FP-injective left B-modules, and
![](https://image.hanspub.org/IMAGE/Edit_72ec98e4-1b3e-4f7e-860f-613acb6d8e67.png)
is an epimorphism.