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arXiv · 2608.13898

Mittag-Leffler Conditions, Gorenstein Modules and Homological Invariants

Guocheng Dai·Xiaolei Zhang
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Abstract

In this paper, we investigate certain properties on the Mittag-Leffler conditions via set-theoretic methods. We establish that a strongly $\aleph_1$-presented module $M$ satisfying Ext$_R^{\ge 1}(M,D^{(\aleph_1)})=0$ belongs to the left orthogonal class of $\overline{D}$, where $\overline{D}$ is the definable of $D$. This yields the consequence that every $\aleph_1$-generated strongly Gorenstein projective module is Gorenstein flat. Furthermore, we investigate when a flat Gorenstein projective module is projective. Finally, for any two-sided $\aleph_1$-coherent ring $R$, we prove the identity $\operatorname{silp}R+\operatorname{silp}R^{\mathrm{op}}=\operatorname{spli}R+\operatorname{spli}R^{\mathrm{op}}$.

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Guocheng Dai, Xiaolei Zhang. 2026-08-14. Mittag-Leffler Conditions, Gorenstein Modules and Homological Invariants. https://arxiv.org/abs/2608.13898

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