Publication details
Relative injective modules, superstability and noetherian categories
| Authors | |
|---|---|
| Year of publication | 2026 |
| Type | Peer-reviewed scientific article |
| Magazine / Source | JOURNAL OF MATHEMATICAL LOGIC |
| MU Faculty or unit | |
| Citation | |
| web | https://www.worldscientific.com/doi/10.1142/S0219061324500272 |
| Doi | https://doi.org/10.1142/S0219061324500272 |
| Keywords | Relative injective modules; Baer criterion; stable independence relation; superstability; noetherian categories; abstract elementary classes |
| Description | We study classes of modules closed under direct sums, M-submodules and M-epimorphic images where M is either the class of embeddings, RD-embeddings or pure embeddings. We show that the M-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and s-torsion pure injective modules satisfy this criterion. The argument presented is a model theoretic one. We use in an essential way stable independence relations which generalize Shelah's non-forking to abstract elementary classes. We show that the classical model theoretic notion of superstability is equivalent to the algebraic notion of a noetherian category for these classes. We use this equivalence to characterize noetherian rings, pure semisimple rings, perfect rings and finite products of finite rings and artinian valuation rings via superstability. |
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