{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3HMKFUAFRTQHMJQLZLO3YLBW67","short_pith_number":"pith:3HMKFUAF","schema_version":"1.0","canonical_sha256":"d9d8a2d0058ce076260bcaddbc2c36f7e481a9b2ae019e4f8410f36a08fed3bf","source":{"kind":"arxiv","id":"1703.01796","version":3},"attestation_state":"computed","paper":{"title":"Annihilators in $\\mathbb{N}^k$-graded and $\\mathbb{Z}^k$-graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Thomas Huettemann","submitted_at":"2017-03-06T10:03:00Z","abstract_excerpt":"It has been shown by McCoy that a right ideal of a polynomial ring with several indeterminates has a non-trivial homogeneous right annihilator of degree 0 provided its right annihilator is non-trivial to begin with. In this note, it is documented that any $\\mathbb{N}$-graded ring $R$ has a slightly weaker property: the right annihilator of a right ideal contains a homogeneous non-zero element, if it is non-trivial to begin with. If $R$ is a subring of a $\\mathbb{Z}^k$ -graded ring $S$ satisfying a certain non-annihilation property (which is the case if $S$ is strongly graded, for example), the"},"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":"1703.01796","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-06T10:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"269bb3ac6eb77b8c0f854655bdd0881e991d1c62ba9c94c73bf22899d9df00ff","abstract_canon_sha256":"1eca6db9a7f80db4eaf2fb477695f7d8dcbf1a17da43ad4769b87d0ee8484e01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:30.371439Z","signature_b64":"nTsvdadAVESdwe+1L+r6UPkfdd8ZKlybemsyFcY/F6swLHsDJ7ISGNrzuhFdGbDJRNgwH3ienT7DR4Xx1DfWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9d8a2d0058ce076260bcaddbc2c36f7e481a9b2ae019e4f8410f36a08fed3bf","last_reissued_at":"2026-05-18T00:26:30.370729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:30.370729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Annihilators in $\\mathbb{N}^k$-graded and $\\mathbb{Z}^k$-graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Thomas Huettemann","submitted_at":"2017-03-06T10:03:00Z","abstract_excerpt":"It has been shown by McCoy that a right ideal of a polynomial ring with several indeterminates has a non-trivial homogeneous right annihilator of degree 0 provided its right annihilator is non-trivial to begin with. In this note, it is documented that any $\\mathbb{N}$-graded ring $R$ has a slightly weaker property: the right annihilator of a right ideal contains a homogeneous non-zero element, if it is non-trivial to begin with. If $R$ is a subring of a $\\mathbb{Z}^k$ -graded ring $S$ satisfying a certain non-annihilation property (which is the case if $S$ is strongly graded, for example), the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01796","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.01796","created_at":"2026-05-18T00:26:30.370858+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.01796v3","created_at":"2026-05-18T00:26:30.370858+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01796","created_at":"2026-05-18T00:26:30.370858+00:00"},{"alias_kind":"pith_short_12","alias_value":"3HMKFUAFRTQH","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3HMKFUAFRTQHMJQL","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3HMKFUAF","created_at":"2026-05-18T12:30:58.224056+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67","json":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67.json","graph_json":"https://pith.science/api/pith-number/3HMKFUAFRTQHMJQLZLO3YLBW67/graph.json","events_json":"https://pith.science/api/pith-number/3HMKFUAFRTQHMJQLZLO3YLBW67/events.json","paper":"https://pith.science/paper/3HMKFUAF"},"agent_actions":{"view_html":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67","download_json":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67.json","view_paper":"https://pith.science/paper/3HMKFUAF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.01796&json=true","fetch_graph":"https://pith.science/api/pith-number/3HMKFUAFRTQHMJQLZLO3YLBW67/graph.json","fetch_events":"https://pith.science/api/pith-number/3HMKFUAFRTQHMJQLZLO3YLBW67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67/action/storage_attestation","attest_author":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67/action/author_attestation","sign_citation":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67/action/citation_signature","submit_replication":"https://pith.science/pith/3HMKFUAFRTQHMJQLZLO3YLBW67/action/replication_record"}},"created_at":"2026-05-18T00:26:30.370858+00:00","updated_at":"2026-05-18T00:26:30.370858+00:00"}