Notes on Gorenstein Flat Modules
Notes on Gorenstein Flat Modules
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DOI：
10.1007/s41980-018-0135-5
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发表时间：
2018-10
影响因子：
0.7
通讯作者：
Yanjiong Yang;Xiaoguang Yan
中科院分区：
文献类型：
--
作者：
Yanjiong Yang;Xiaoguang Yan
本文研究了Gorenstein平坦模是Gorenstein投射模的条件。证明了完全环上可数表现的强Gorenstein平坦模都是Gorenstein投射模。进一步证明了如果基环Ris-纯内射为R-模，则Gorenstein平坦模类与Gorenstein投射模类重合，从而所有模都有Gorenstein投射覆盖.作为推论，我们利用Gorenstein投射模和Gorenstein平坦模给出了凝聚完备环的一个刻画。
In this paper, we explore conditions under which Gorenstein flat modules are Gorenstein projective. We prove that all countably presented strongly Gorenstein flat modules are Gorenstein projective over perfect rings. Moreover, we show that if the base ringRis-pure injective as anR-module, then the class of Gorenstein flat modules coincides with the class of Gorenstein projective modules, and hence all modules have Gorenstein projective covers. And as a corollary, we give a characterization of coherent perfect rings by Gorenstein projective and Gorenstein flat modules.