A strongly compact cardinal yields a left and right coherent ring with $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$

Abstract

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 $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$.

Disclosure

“with PGF (R) ̸= GP(R). It also assisted in weakening the strongly compact cardinal hypothesis to the local ultrafilter hypothesis LUH and in strengthening the construc- tion from a one-sided coherent ring to a left and right coherent ring. GPT-5.6 Sol was used for an additional adversarial review and revision of the manuscript. The author independently verified all mathematical statements, proofs, and citations in the final manuscript and takes full responsibility for its content.”

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Classification

Substantial mathematical content or result generation

Multiplier

10

Verified

2026-08-23T05:23:03.090172Z

Structural counts