Flat Gorenstein projective modules and projectivity

Determine whether every flat Gorenstein projective module over an arbitrary ring is projective.

Background

The paper studies the unresolved equality between the class of projective modules and the class of flat Gorenstein projective modules. It proves projectivity under several additional hypotheses, including when the module is a direct limit of projectives over an index set of cardinality less than ℵω, but the unrestricted question remains unresolved.

References

Another open problem, raised by Bazzoni et al. , asks whether every flat Gorenstein projective module is projective.

— Mittag-Leffler Conditions, Gorenstein Modules and Homological Invariants  (2608.13898 - Dai et al., 14 Aug 2026) in Introduction; Section 3, before Lemma \ref{gpgfplfgp}