{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UZQJBU7UYKXAB72JOL6JEUFI5Y","short_pith_number":"pith:UZQJBU7U","schema_version":"1.0","canonical_sha256":"a66090d3f4c2ae00ff4972fc9250a8ee1091d0b49064a2171d71197a9344e8c0","source":{"kind":"arxiv","id":"1707.09290","version":1},"attestation_state":"computed","paper":{"title":"Zero action determined modules for associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Wei Hu, Zhankui Xiao","submitted_at":"2017-07-28T15:49:02Z","abstract_excerpt":"Let $A$ be a unital associative algebra over a field $F$ and $V$ be a unital left $A$-module. The module $V$ is called zero action determined if every bilinear map $f: A\\times V\\rightarrow F$ with the property that $f(a,m)=0$ whenever $am=0$ is of the form $f(x,v)=\\Phi(xv)$ for some linear map $\\Phi: V\\rightarrow F$. In this paper, we classify the finite dimensional irreducible and principal projective zero action determined modules of $A$. As an application, two classes of zero product determined algebras are shown: some semiperfect algebras (infinite dimensional in general); quasi-hereditary"},"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":"1707.09290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-07-28T15:49:02Z","cross_cats_sorted":[],"title_canon_sha256":"4e6ede11d7936d1fccd54bc374b10159c2979e03d29e77a8a6fa008e3af71e6e","abstract_canon_sha256":"124387db1f59a8b17ed6e9820ec50e3d1eda9531d97d76a57a51a58fa20692d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:16.576377Z","signature_b64":"toQcAbzTMKWHfOycvfS4dTT7TF4HyhxA4ooi1EcVn6aI1zui5AIBC22Hfsy9e8fE0AjNT9z8tvU6NCa94qlcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a66090d3f4c2ae00ff4972fc9250a8ee1091d0b49064a2171d71197a9344e8c0","last_reissued_at":"2026-05-18T00:39:16.575755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:16.575755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zero action determined modules for associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Wei Hu, Zhankui Xiao","submitted_at":"2017-07-28T15:49:02Z","abstract_excerpt":"Let $A$ be a unital associative algebra over a field $F$ and $V$ be a unital left $A$-module. The module $V$ is called zero action determined if every bilinear map $f: A\\times V\\rightarrow F$ with the property that $f(a,m)=0$ whenever $am=0$ is of the form $f(x,v)=\\Phi(xv)$ for some linear map $\\Phi: V\\rightarrow F$. In this paper, we classify the finite dimensional irreducible and principal projective zero action determined modules of $A$. As an application, two classes of zero product determined algebras are shown: some semiperfect algebras (infinite dimensional in general); quasi-hereditary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09290","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.09290","created_at":"2026-05-18T00:39:16.575835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.09290v1","created_at":"2026-05-18T00:39:16.575835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09290","created_at":"2026-05-18T00:39:16.575835+00:00"},{"alias_kind":"pith_short_12","alias_value":"UZQJBU7UYKXA","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"UZQJBU7UYKXAB72J","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"UZQJBU7U","created_at":"2026-05-18T12:31:49.984773+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/UZQJBU7UYKXAB72JOL6JEUFI5Y","json":"https://pith.science/pith/UZQJBU7UYKXAB72JOL6JEUFI5Y.json","graph_json":"https://pith.science/api/pith-number/UZQJBU7UYKXAB72JOL6JEUFI5Y/graph.json","events_json":"https://pith.science/api/pith-number/UZQJBU7UYKXAB72JOL6JEUFI5Y/events.json","paper":"https://pith.science/paper/UZQJBU7U"},"agent_actions":{"view_html":"https://pith.science/pith/UZQJBU7UYKXAB72JOL6JEUFI5Y","download_json":"https://pith.science/pith/UZQJBU7UYKXAB72JOL6JEUFI5Y.json","view_paper":"https://pith.science/paper/UZQJBU7U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.09290&json=true","fetch_graph":"https://pith.science/api/pith-number/UZQJBU7UYKXAB72JOL6JEUFI5Y/graph.json","fetch_events":"https://pith.science/api/pith-number/UZQJBU7UYKXAB72JOL6JEUFI5Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UZQJBU7UYKXAB72JOL6JEUFI5Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UZQJBU7UYKXAB72JOL6JEUFI5Y/action/storage_attestation","attest_author":"https://pith.science/pith/UZQJBU7UYKXAB72JOL6JEUFI5Y/action/author_attestation","sign_citation":"https://pith.science/pith/UZQJBU7UYKXAB72JOL6JEUFI5Y/action/citation_signature","submit_replication":"https://pith.science/pith/UZQJBU7UYKXAB72JOL6JEUFI5Y/action/replication_record"}},"created_at":"2026-05-18T00:39:16.575835+00:00","updated_at":"2026-05-18T00:39:16.575835+00:00"}