{"paper":{"title":"Pretty cleanness and filter-regular sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ali Soleyman Jahan, Kamran Divaani-Aazar, Somayeh Bandari","submitted_at":"2013-11-28T12:22:56Z","abstract_excerpt":"Let $K$ be a field and $S=K[x_1,\\ldots, x_n]$. Let $I$ be a monomial ideal of $S$ and $u_1,\\ldots, u_r$ be monomials in $S$ which form a filter-regular sequence on $S/I$. We show that $S/I$ is pretty clean if and only if $S/(I,u_1,\\ldots, u_r)$ is pretty clean."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0858","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"}