Gorenstein Homological Aspects of Monomorphism Categories via Morita Rings
Gorenstein Homological Aspects of Monomorphism Categories via Morita Rings
复制标题
DOI：
10.1007/s10468-016-9652-1
复制
发表时间：
2016-11
影响因子：
0.6
通讯作者：
Nan Gao;Chrysostomos Psaroudakis
中科院分区：
文献类型：
--
作者：
Nan Gao;Chrysostomos Psaroudakis
本文构造了双模同态为零的Morita环上的Gorenstein-投射模，并给出了这类环是Gorenstein-Artin代数的充分条件。这是我们工作的第一部分，它与单态范畴密切相关。在第二部分中，我们研究了域具有有限投射维度的单态。特别是，我们表明，后者的范畴是Gorenstein子范畴的单态范畴的Gorenstein代数。最后，我们考虑范畴的连贯函子的稳定范畴的Gorenstein子范畴，并表明，它进行了结构的Gorenstein阿贝尔范畴。
In this paper we construct Gorenstein-projective modules over Morita rings with zero bimodule homomorphisms and we provide sufficient conditions for such rings to be Gorenstein Artin algebras. This is the first part of our work which is strongly connected with monomorphism categories. In the second part, we investigate monomorphisms where the domain has finite projective dimension. In particular, we show that the latter category is a Gorenstein subcategory of the monomorphism category over a Gorenstein algebra. Finally, we consider the category of coherent functors over the stable category of this Gorenstein subcategory and show that it carries a structure of a Gorenstein abelian category.