On the finiteness of Gorenstein homological dimensions
On the finiteness of Gorenstein homological dimensions
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DOI：
10.1016/j.jalgebra.2012.09.018
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发表时间：
2012-12
影响因子：
0.9
通讯作者：
I. Emmanouil
中科院分区：
文献类型：
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作者：
I. Emmanouil
本文研究了有限Gorenstein射影、内射和平面维模的某些性质。我们检验了所有Gorenstein射影模都是Gorenstein平的条件，并建立了有限Gorenstein射影维模的Gorenstein tor函子的平衡。我们还研究了一类具有有限Gorenstein整体维数和弱维数的环，并根据环的某些上同调不变量计算了这些维数。最后，给出了有限Gorenstein整体和弱维环的一些例子。
In this paper, we study certain properties of modules of finite Gorenstein projective, injective and flat dimensions. We examine conditions which imply that all Gorenstein projective modules are Gorenstein flat and establish the balance of the Gorenstein Tor-functor for modules of finite Gorenstein projective dimension. We also examine the class of rings that have finite Gorenstein global and weak dimensions and compute these dimensions, in terms of certain cohomological invariants of the ring. Finally, we provide some examples of rings of finite Gorenstein global and weak dimensions.