{"paper":{"title":"Symbolic and Ordinary Powers of Ideals in Hibi Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Daniel Smolkin, Janet Page, Kevin Tucker","submitted_at":"2018-09-29T04:54:48Z","abstract_excerpt":"We exhibit a class of Hibi rings which are diagonally F-regular over fields of positive characteristic, and diagonally $F$-regular type over fields of characteristic zero, in the sense of Carvajal-Rojas and Smolkin. It follows that such Hibi rings satisfy the uniform symbolic topology property effectively in all characteristics. Namely, for rings $R$ in this class of Hibi rings, we have $P^{(dn)} \\subseteq P^n$ for all $P \\in \\operatorname{Spec} R$, where $d = \\dim(R)$. Further, we demonstrate that all Hibi rings over fields of positive characteristic are 2-diagonally $F$-regular, and that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00149","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"}