{"paper":{"title":"Approximations of injective modules and finitistic dimension","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","submitted_at":"2015-04-30T15:54:17Z","abstract_excerpt":"Let $\\Lambda$ be an artin algebra and let $\\mathcal{P}^{<\\infty}_\\Lambda$ the category of finitely generated right $\\Lambda$-modules of finite projective dimension. We show that $\\mathcal{P}^{<\\infty}_\\Lambda$ is contravariantly finite in $\\rm mod\\,\\Lambda$ if and only if the direct sum $E$ of the indecomposable Ext-injective modules in $\\mathcal{P}^{<\\infty}_\\Lambda$ form a tilting module in $\\rm mod\\,\\Lambda$. Moreover, we show that in this case $E$ coincides with the direct sum of the minimal right $\\mathcal{P}^{<\\infty}_\\Lambda$-approximations of the indecomposable $\\Lambda$-injective modu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08282","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"}