形式三角矩阵环上的Gorenstein AC-投射维数
Gorenstein AC-Projective Dimensions over Formal Triangular Matrix Rings
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，为左T - 模。 我们利用左A-模M1和左B-模M2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 be a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule, and let 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 M1 and left B-module M2. 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 and Gorenstein AC-projective dimension of the left T(R)-module are described.
文章引用：李帮禹, 杨晓燕. 形式三角矩阵环上的Gorenstein AC-投射维数[J]. 理论数学, 2022, 12(1): 109-116. https://doi.org/10.12677/PM.2022.121015

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