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We show that if $\\alpha$ is global and unital, then $S$ is left (right) artinian if and only if $R$ is left (right) artinian and $R_g = \\{ 0 \\},$ for all but finitely many $g \\in \\textrm{mor}(G)$. We use this result to prove that if $\\alpha$ is unital and $R$ is alternative, then $S$ is left (right) artinian if and only if $R$ is left (right) artinian and $R_g = \\{ 0 "},"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":"1603.02237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-07T20:07:10Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"b2fc79feb01e47ac3197c7abc8824d4a70d64e49ac1cc28c1d7765ccd69ba4d6","abstract_canon_sha256":"ad66a6e282633493af937da84643eeb1ba5fefda932672a9884299a355c42db4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:44.932718Z","signature_b64":"vpbdevaiRaYJXOqOCG32uK49hGMgjYfD/3ZGCnUoHoxHNFfj7SAHUg2eSNBv1WU/gb2Cz7+tibEus+HHjF6aBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed148d3958535e663decea1bd1f665c66396d90a87f9b8b8955defb699797abe","last_reissued_at":"2026-05-18T01:02:44.932309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:44.932309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Artinian and noetherian partial skew groupoid rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"H\\'ector Pinedo, Johan \\\"Oinert, Patrik Nystedt","submitted_at":"2016-03-07T20:07:10Z","abstract_excerpt":"Let $\\alpha = \\{ \\alpha_g : R_{g^{-1}} \\rightarrow R_g \\}_{g \\in \\textrm{mor}(G)}$ be a partial action of a groupoid $G$ on a non-associative ring $R$ and let $S = R \\star_{\\alpha} G$ be the associated partial skew groupoid ring. We show that if $\\alpha$ is global and unital, then $S$ is left (right) artinian if and only if $R$ is left (right) artinian and $R_g = \\{ 0 \\},$ for all but finitely many $g \\in \\textrm{mor}(G)$. We use this result to prove that if $\\alpha$ is unital and $R$ is alternative, then $S$ is left (right) artinian if and only if $R$ is left (right) artinian and $R_g = \\{ 0 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02237","kind":"arxiv","version":2},"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":"1603.02237","created_at":"2026-05-18T01:02:44.932379+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.02237v2","created_at":"2026-05-18T01:02:44.932379+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02237","created_at":"2026-05-18T01:02:44.932379+00:00"},{"alias_kind":"pith_short_12","alias_value":"5UKI2OKYKNPG","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5UKI2OKYKNPGMPPM","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5UKI2OKY","created_at":"2026-05-18T12:30:01.593930+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/5UKI2OKYKNPGMPPM5IN5D5TFYZ","json":"https://pith.science/pith/5UKI2OKYKNPGMPPM5IN5D5TFYZ.json","graph_json":"https://pith.science/api/pith-number/5UKI2OKYKNPGMPPM5IN5D5TFYZ/graph.json","events_json":"https://pith.science/api/pith-number/5UKI2OKYKNPGMPPM5IN5D5TFYZ/events.json","paper":"https://pith.science/paper/5UKI2OKY"},"agent_actions":{"view_html":"https://pith.science/pith/5UKI2OKYKNPGMPPM5IN5D5TFYZ","download_json":"https://pith.science/pith/5UKI2OKYKNPGMPPM5IN5D5TFYZ.json","view_paper":"https://pith.science/paper/5UKI2OKY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.02237&json=true","fetch_graph":"https://pith.science/api/pith-number/5UKI2OKYKNPGMPPM5IN5D5TFYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/5UKI2OKYKNPGMPPM5IN5D5TFYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5UKI2OKYKNPGMPPM5IN5D5TFYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5UKI2OKYKNPGMPPM5IN5D5TFYZ/action/storage_attestation","attest_author":"https://pith.science/pith/5UKI2OKYKNPGMPPM5IN5D5TFYZ/action/author_attestation","sign_citation":"https://pith.science/pith/5UKI2OKYKNPGMPPM5IN5D5TFYZ/action/citation_signature","submit_replication":"https://pith.science/pith/5UKI2OKYKNPGMPPM5IN5D5TFYZ/action/replication_record"}},"created_at":"2026-05-18T01:02:44.932379+00:00","updated_at":"2026-05-18T01:02:44.932379+00:00"}