{"paper":{"title":"Split-by-nilpotent extensions algebras and stratifying systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Corina S\\'aenz, Marcelo Lanzilotta, Octavio Mendoza","submitted_at":"2013-04-19T00:52:13Z","abstract_excerpt":"Let $\\Gamma$ and $\\Lambda$ be artin algebras such that $\\Gamma$ is a split-by-nilpotent extension of $\\Lambda$ by a two sided ideal $I$ of $\\Gamma.$ Consider the so-called change of rings functors $G:={}_\\Gamma\\Gamma_\\Lambda\\otimes_\\Lambda -$ and $F:={}_\\Lambda \\Lambda_\\Gamma\\otimes_\\Gamma -.$ In this paper, we find the necessary and sufficient conditions under which a stratifying system $(\\Theta,\\leq)$ in $\\modu\\Lambda$ can be lifted to a stratifying system $(G\\Theta,\\leq)$ in $\\modu\\,(\\Gamma).$ Furthermore, by using the functors $F$ and $G,$ we study the relationship between their filtered c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5289","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"}