摘要:
本文研究了形式三角矩阵环上Gorenstein AC-投射维数的问题。 令
![](https://image.hanspub.org/IMAGE/Edit_3c047687-fe6b-4c24-afcb-df3d59ce1688.png)
为一个形式三角矩阵环,其中A和B为环,U为一个(B,A)-双模,
![](https://image.hanspub.org/IMAGE/Edit_df459b52-7dd6-46f4-ac77-a55dd1a885bc.png)
为左T - 模。 我们利用左A-模M
1和左B-模M
2的Gorenstein AC-投射维数,通过构造左T-模正合序列的方法给出了
TM的Gorenstein AC-投射维数的刻画,进而建立了环A,环B和环T的左整体Gorenstein AC-投射维数之间的关系。 作为这些结论的应用,我们刻画了环
![](https://image.hanspub.org/IMAGE/Edit_5e1f0238-dea6-49e8-b4ed-44b725d022e9.png)
的左整体Gorenstein AC-投射维数及该环上左模的Gorenstein AC-投射维数。
Abstract:
This paper considers Gorenstein AC-projective dimensions over formal triangular matrix rings. Let
![](https://image.hanspub.org/IMAGE/Edit_302fa29e-fa50-46c8-8683-905a0da5c6ad.png)
be a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule, and let
![](https://image.hanspub.org/IMAGE/Edit_11333728-3855-4d35-83f0-eb2b214dbec1.png)
be a left T-module. By constructing exact sequences, we characterize Gorenstein AC-projective dimensions of a left T-module
TM with Gorenstein AC-projective dimensions of left A-module M
1 and left B-module M
2. Moreover, we establish a relationship of left global Gorenstein AC-projective dimensions of ring T and A, B. As an application of above conclusions, left global Gorenstein AC-projective dimension of the ring
![](https://image.hanspub.org/IMAGE/Edit_b4a8c55c-2f78-4467-b134-87af1a8b4c52.png)
and Gorenstein AC-projective dimension of the left T(R)-module are described.