强紧致基数给出一个左右凝聚环，满足$\boldsymbol{\text{PGF}}(R)\boldsymbol{\neq}\boldsymbol{\text{GP}}(R)$
A strongly compact cardinal yields a left and right coherent ring with $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$
AI总结：
在局部布尔-鲁斯假设$\textsf{LBR}$下，构造出左右凝聚环$R$，证明了$\text{PGF}(R)$是$\text{GP}(R)$的真子类，明确了Gorenstein同调代数中相关模类的包含关系。
AI中文摘要：
对于环$R$，令$\boldsymbol{\text{GP}}(R)$、$\boldsymbol{\text{GF}}(R)$、$\boldsymbol{\text{PGF}}(R)$分别表示Gorenstein投射、Gorenstein平坦、可解Gorenstein平坦左$R$-模的类。我们引入局部布尔-鲁斯假设$\textsf{LBR}$：强紧致基数的存在性蕴含$\textsf{LBR}$，而$\textsf{LBR}$蕴含可测基数的存在性。在假设$\textsf{LBR}$的前提下，我们构造了一个左右凝聚环$R$，以及一个非Gorenstein平坦的强Gorenstein投射左$R$-模$G$，由此得到$\boldsymbol{\text{PGF}}(R)\boldsymbol{\neq}\boldsymbol{\text{GP}}(R)$。
英文摘要：
For a ring $R$, let $\mathcal{GP}(R)$, $\mathcal{GF}(R)$, and $\mathcal{PGF}(R)$ denote the classes of Gorenstein projective, Gorenstein flat, and projectively coresolved Gorenstein flat left $R$-modules, respectively. We isolate the local ultrafilter hypothesis $\textsf{LUH}$: the existence of a strongly compact cardinal implies $\textsf{LUH}$, while $\textsf{LUH}$ implies the existence of a measurable cardinal. Assuming $\textsf{LUH}$, we construct a left and right coherent ring $R$ and a strongly Gorenstein projective left $R$-module $G$ which is not Gorenstein flat; hence $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$.
