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arXiv · 2512.17799

Deconstructible classes of modules and stability

Marcos Mazari-Armida·Jan Trlifaj
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Abstract

We show that every deconstructible class of modules with all embeddings, all pure embedding and all RD-embeddings is stable. The argument is presented in the context of abstract classes of modules without amalgamation and the key idea is to construct a stable-like independence relation. In particular, the following classes of modules with all embeddings, all pure embedding and all RD-embeddings are shown to be stable: all free and torsion-free modules over any ring, and for each $n \geq 0$, the classes of all modules of projective and flat dimension $\leq n$ over any ring, and the class of all modules of injective dimension $\leq n$ over any right noetherian ring.

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Marcos Mazari-Armida, Jan Trlifaj. 2026-07-10. Deconstructible classes of modules and stability. https://arxiv.org/abs/2512.17799

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