{"paper":{"title":"$\\star $-super potent domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Evan Houston, Muhammad Zafrullah","submitted_at":"2017-12-19T00:28:14Z","abstract_excerpt":"For a finite-type star operation $\\star$ on a domain $R$, we say that $R$ is $\\star$-super potent if each maximal $\\star$-ideal of $R$ contains a finitely generated ideal $I$ such that (1) $I$ is contained in no other maximal $\\star$-ideal of $R$ and (2) $J$ is $\\star$-invertible for every finitely generated ideal $J \\supseteq I$. Examples of $t$-super potent domains include domains each of whose maximal $t$-ideals is $t$-invertible (e.g., Krull domains). We show that if the domain $R$ is $\\star$-super potent for some finite-type star operation $\\star$, then $R$ is $t$-super potent, we study $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06725","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"}