关于Gorenstein AC-余挠模

On Gorenstein AC-cotorsion modules

引入Gorenstein AC-余挠模的概念,该模是介于Gorenstein余挠模类和余挠模类之间的一种模类;讨论Gorenstein AC-余挠模的诸多性质,如Gorenstein AC-余挠模与平坦模、Gorenstein AC-平坦模之间的关系;用Gorenstein AC-余挠模刻画每个R-模是Gorenstein AC-平坦模的环类;最后讨论Gorenstein AC-余挠包、Gorenstein AC-平坦盖的存在性,还讨论了每个R-模是Gorenstein AC-余挠模的条件.

The concept of Gorenstein AC-cotorsion modules was introduced,which is a kind of module between Gorenstein cotorsion modules and cotorsion modules.Some properties of Gorenstein AC-cotorsion modules were discussed,such as the connections between Gorenstein weak cotorsion modules,flat modules and Gorenstein weak flat modules.The condition in which every R-module was Gorenstein AC-flat was discussed in terms of Gorenstein AC-cotorsion modules.Finally,the existence of Gorenstein AC-cotorsion envelopes and Gorenstein AC-flat covers were discussed.The condition in which every R-module was Gorenstein AC-cotorsion module was also discussed.