投射余可解的Gorenstein平坦模和Gorenstein AC投射模
Projectively Coresolved Gorenstein Flat Modules and Gorenstein AC Projective Modules
摘要: 本文我们给出了Gorenstein AC投射模的类与投射余可解的Gorenstein平坦模的类等价的条件，证明了在凝聚环R上，Gorenstein AC投射模的类，投射余可解的Gorenstein平坦模的类与Ding投射模的类等价。同时也给出了Gorenstein AC投射模的类与Gorenstein投射模的类等价的充分必要条件，证明了在任意环R上，Gorenstein AC投射模的类与Gorenstein投射模的类等价当且仅当Level模的类包含在Gorenstein投射模的类的右正交中。最后我们给出了Gorenstein AC投射模的类与Gorenstein投射模的类在凝聚环上等价的一些充分必要条件。
Abstract: In this paper, we give a condition in order for the class of Gorenstein AC projective modules to co-incide with the class of projectively coresolved Gorenstein flat modules, we prove that the class of Gorenstein AC projective modules equal to the class of projectively coresolved Gorenstein flat modules equal to the class of Ding projective modules over coherent rings. We also give a necessary and sufficient condition in order for the class of Gorenstein AC projective modules to coincide with the class of Gorenstein projective modules, we prove that the class of Gorenstein AC projective modules to coincide with the class of Gorenstein projective modules if and only if the class of level modules belongs to the right orthogonal class with respect to Gorenstein projective modules. And we give some necessary and sufficient conditions in order for the class of Gorenstein AC projective modules to coincide with the class of Gorenstein projective modules over coherent rings.
文章引用：刘欢, 杨晓燕. 投射余可解的Gorenstein平坦模和Gorenstein AC投射模[J]. 理论数学, 2021, 11(4): 606-611. https://doi.org/10.12677/PM.2021.114074

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