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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.08353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-23T00:12:39Z","cross_cats_sorted":[],"title_canon_sha256":"c507a290c1e8cd8995f4bd549d4625fdbc9c22be72e8c6b8bb9537dad87dc64e","abstract_canon_sha256":"7d7b9db0ab7ea49c0b4e309048c4b098ffe9b90ce00793f650635151fd3deecd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:43.908648Z","signature_b64":"yArEsZsqG6FiZISN3DUnqGOnv8DwQuMejlny00/Hki6JnnOzI016I5GrbuY3M8RKS56hQVSxdte/PWxKafLjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a39cd2c5f6b94d828659c01365d425c69473ee05e4062719f108ec49b698b57","last_reissued_at":"2026-05-18T00:22:43.908204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:43.908204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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