{"paper":{"title":"Self-injective right artinian rings and Igusa Todorov functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fran\\c{c}ois Huard, Marcelo Lanzilotta","submitted_at":"2011-01-10T19:43:07Z","abstract_excerpt":"We show that a right artinian ring $R$ is right self-injective if and only if $\\psi(M)=0$ (or equivalently $\\phi(M)=0$) for all finitely generated right $R$-modules $M$, where $\\psi, \\phi : \\mod R \\to \\mathbb N$ are functions defined by Igusa and Todorov. In particular, an artin algebra $\\Lambda$ is self-injective if and only if $\\phi(M)=0$ for all finitely generated right $\\Lambda$-modules $M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1936","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"}