Deconstructible classes of modules and stability
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917157977194496 |
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| author | Mazari-Armida, Marcos Trlifaj, Jan |
| author_facet | Mazari-Armida, Marcos Trlifaj, Jan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deconstructible classes of modules and stability Mazari-Armida, Marcos Trlifaj, Jan Logic Rings and Algebras Primary: 03C48, 16E30. Secondary: 03C45, 03C60, 16D90, 13L05 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. |
| title | Deconstructible classes of modules and stability |
| topic | Logic Rings and Algebras Primary: 03C48, 16E30. Secondary: 03C45, 03C60, 16D90, 13L05 |
| url | https://arxiv.org/abs/2512.17799 |