{"paper":{"title":"Filtering subcategories of modules of an artinian algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Smith, Fran\\c{c}ois Huard, Marcelo Lanzilotta","submitted_at":"2015-05-26T15:59:36Z","abstract_excerpt":"Let $A$ be an artinian algebra, and let $\\mathcal{C}$ be a subcategory of mod$A$ that is closed under extensions. When $\\mathcal{C}$ is closed under kernels of epimorphisms (or closed under cokernels of monomorphisms), we describe the smallest class of modules that filters $\\mathcal{C}$. As a consequence, we obtain sufficient conditions for the finitistic dimension of an algebra over a field to be finite. We also apply our results to the torsion pairs. In particular, when a torsion pair is induced by a tilting module, we show that the smallest classes of modules that filter the torsion and tor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07025","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"}