{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:JK75XYJCW7ABPE5OTKCLFE35Z4","short_pith_number":"pith:JK75XYJC","schema_version":"1.0","canonical_sha256":"4abfdbe122b7c01793ae9a84b2937dcf37b769679319d1a661ab0bc0d4e288af","source":{"kind":"arxiv","id":"0903.4514","version":3},"attestation_state":"computed","paper":{"title":"Gorenstein Syzygy Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Chonghui Huang, Zhaoyong Huang","submitted_at":"2009-03-26T05:32:53Z","abstract_excerpt":"For any ring $R$ and any positive integer $n$, we prove that a left $R$-module is a Gorenstein $n$-syzygy if and only if it is an $n$-syzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of finitely generated modules. We prove that a module $M\\in \\mod R^{op}$ is a Gorenstein transpose of a module $A\\in \\mod R$ if and only if $M$ can be embedded into a transpose of $A$ with the cokernel Gorenstein projective. Some applications of this result are given."},"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":"0903.4514","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-26T05:32:53Z","cross_cats_sorted":[],"title_canon_sha256":"368cd17e6426d25256440e8f46f9e19009ee7686bd6bfa6aff3ce6e7511432d5","abstract_canon_sha256":"085711676c292d66092589003583ec2d5c2a52bbe426755dc572a7186dabf8a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:18.424583Z","signature_b64":"8auG425mQqgBCGzVTX/N1zjw2YZ/TOKITlkEwhx2SeO2JG42Qny6ADv6wWxivHAXLr3AqyHVE0euGCcRdFVlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4abfdbe122b7c01793ae9a84b2937dcf37b769679319d1a661ab0bc0d4e288af","last_reissued_at":"2026-05-18T04:39:18.422234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:18.422234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gorenstein Syzygy Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Chonghui Huang, Zhaoyong Huang","submitted_at":"2009-03-26T05:32:53Z","abstract_excerpt":"For any ring $R$ and any positive integer $n$, we prove that a left $R$-module is a Gorenstein $n$-syzygy if and only if it is an $n$-syzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of finitely generated modules. We prove that a module $M\\in \\mod R^{op}$ is a Gorenstein transpose of a module $A\\in \\mod R$ if and only if $M$ can be embedded into a transpose of $A$ with the cokernel Gorenstein projective. Some applications of this result are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4514","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":"0903.4514","created_at":"2026-05-18T04:39:18.422388+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.4514v3","created_at":"2026-05-18T04:39:18.422388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4514","created_at":"2026-05-18T04:39:18.422388+00:00"},{"alias_kind":"pith_short_12","alias_value":"JK75XYJCW7AB","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"JK75XYJCW7ABPE5O","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"JK75XYJC","created_at":"2026-05-18T12:26:00.592388+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/JK75XYJCW7ABPE5OTKCLFE35Z4","json":"https://pith.science/pith/JK75XYJCW7ABPE5OTKCLFE35Z4.json","graph_json":"https://pith.science/api/pith-number/JK75XYJCW7ABPE5OTKCLFE35Z4/graph.json","events_json":"https://pith.science/api/pith-number/JK75XYJCW7ABPE5OTKCLFE35Z4/events.json","paper":"https://pith.science/paper/JK75XYJC"},"agent_actions":{"view_html":"https://pith.science/pith/JK75XYJCW7ABPE5OTKCLFE35Z4","download_json":"https://pith.science/pith/JK75XYJCW7ABPE5OTKCLFE35Z4.json","view_paper":"https://pith.science/paper/JK75XYJC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.4514&json=true","fetch_graph":"https://pith.science/api/pith-number/JK75XYJCW7ABPE5OTKCLFE35Z4/graph.json","fetch_events":"https://pith.science/api/pith-number/JK75XYJCW7ABPE5OTKCLFE35Z4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JK75XYJCW7ABPE5OTKCLFE35Z4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JK75XYJCW7ABPE5OTKCLFE35Z4/action/storage_attestation","attest_author":"https://pith.science/pith/JK75XYJCW7ABPE5OTKCLFE35Z4/action/author_attestation","sign_citation":"https://pith.science/pith/JK75XYJCW7ABPE5OTKCLFE35Z4/action/citation_signature","submit_replication":"https://pith.science/pith/JK75XYJCW7ABPE5OTKCLFE35Z4/action/replication_record"}},"created_at":"2026-05-18T04:39:18.422388+00:00","updated_at":"2026-05-18T04:39:18.422388+00:00"}