{"paper":{"title":"Relative Igusa-Todorov functions and relative homological dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Marcelo Lanzilotta, Octavio Mendoza","submitted_at":"2016-08-16T16:07:13Z","abstract_excerpt":"We develope the theory of the $\\mathcal{E}$-relative Igusa-Todorov functions in an exact $ IT$-context $(\\mathcal{C},\\mathcal{E}).$ In the case when $\\mathcal{C}=$mod$\\, (\\Lambda)$ is the category of finitely generated left $\\Lambda$-modules, for an artin algebra $\\Lambda,$ and $\\mathcal{E}$ is the class of all exact sequences in $\\mathcal{C},$ we recover the usual Igusa-Todorov functions. We use the setting of the exact structures and the Auslander-Solberg relative homological theory to generalise the original Igusa-Todorov's results. Furthermore, we introduce the $\\mathcal{E}$-relative Igusa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04649","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"}