{"paper":{"title":"On $\\ast $-Semi Homogeneous Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Daniel D. Anderson, Muhammad Zafrullah","submitted_at":"2018-02-23T00:12:39Z","abstract_excerpt":"Let $\\ast $ be a finite character star operation defined on an integral domain $D.$ Call a nonzero $\\ast $-ideal $I$ of finite type a $\\ast $ -homogeneous ($\\ast $-homog) ideal, if $I\\subsetneq D$ and $(J+K)^{\\ast }\\neq D$ for every pair $D\\supsetneq J,K\\supseteq I$ of proper $\\ast $ -ideals of finite type$.$ Call an integral domain $D$ a $\\ast $-Semi Homogeneous Domain ($\\ast $-SHD) if every proper principal ideal $xD$ of $D$ is expressible as a $\\ast $-product of finitely many $\\ast $-homog ideals. We show that a $\\ast $-SHD contains a family $\\mathcal{F}$ of prime ideals such that (a) $D=\\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08353","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"}