{"paper":{"title":"Maximal ideals in module categories and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alberto Facchini, Manuel Cort\\'es-Izurdiaga","submitted_at":"2017-10-19T09:31:20Z","abstract_excerpt":"We study the existence of maximal ideals in preadditive categories defining an order $\\preceq$ between objects, in such a way that if there do not exist maximal objects with respect to $\\preceq$, then there is no maximal ideal in the category. In our study, it is sometimes sufficient to restrict our attention to suitable subcategories. We give an example of a category $\\mathbf C_F$ of modules over a right noetherian ring $R$ in which there is a unique maximal ideal. The category $\\mathbf C_F$ is related to an indecomposable injective module $F$, and the objects of $\\mathbf C_F$ are the $R$-mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07053","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}