{"paper":{"title":"The Phi-dimension: A new homological measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Marcelo Lanzilotta, Octavio Mendoza, Sonia Fernandes","submitted_at":"2013-04-02T19:59:36Z","abstract_excerpt":"K. Igusa and G. Todorov introduced two functions $\\phi$ and $\\psi,$ which are natural and important homological measures generalising the notion of the projective dimension. These Igusa-Todorov functions have become into a powerful tool to understand better the finitistic dimension conjecture.\n  In this paper, for an artin $R$-algebra $A$ and the Igusa-Todorov function $\\phi,$ we characterise the $\\phi$-dimension of $A$ in terms either of the bi-functors $\\mathrm{Ext}^{i}_{A}(-, -)$ or Tor's bi-functors $\\mathrm{Tor}^{A}_{i}(-,-).$ Furthermore, by using the first characterisation of the $\\phi$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0754","kind":"arxiv","version":2},"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"}