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This definition generalizes (locally)projective covers. We characterize $I$-semiregular and $I$-semiperfect rings which are defined by Yousif and Zhou [19] using (locally)projective $I$-covers in section 2 and 3. $I$-semiregular and $I$-semiperfect rings are characterized by projec"},"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":"1108.2083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-08-10T02:16:25Z","cross_cats_sorted":[],"title_canon_sha256":"29de31e9aceb9aceec845062fe3ee5e4a8a77a73dc7b0843f76f58cb70166e79","abstract_canon_sha256":"d96b681b8f9a120fa770ac9cd5ec100147b885c223f4a528686b7429d8cc5255"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:49.392548Z","signature_b64":"apKfBuZ8j72xDx1ccD/SGXR8+VP9DnayMj42jN8e5g54JAC2I+zLaXyPbIr8HxUzoKhrX5GUU4PrqXowZRqSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1a397f33cff28f8e8640c67d0bdea8b380f1f3017d856e77fffe076a9eb464f","last_reissued_at":"2026-05-18T04:15:49.392020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:49.392020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of I-semiregular and I-semiperfect rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Yongduo Wang","submitted_at":"2011-08-10T02:16:25Z","abstract_excerpt":"Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. We call $(P, f)$ a (locally)projective $I$-cover of $M$ if $f$ is an epimorphism from $P$ to $M$, $P$ is (locally)projective, $Kerf\\subseteq IP$, and whenever $P=Kerf+X$, then there is a projective summand $Y$ of $P$ in $Kerf$ such that $P=Y\\oplus X$. This definition generalizes (locally)projective covers. We characterize $I$-semiregular and $I$-semiperfect rings which are defined by Yousif and Zhou [19] using (locally)projective $I$-covers in section 2 and 3. $I$-semiregular and $I$-semiperfect rings are characterized by projec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2083","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":"1108.2083","created_at":"2026-05-18T04:15:49.392101+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2083v1","created_at":"2026-05-18T04:15:49.392101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2083","created_at":"2026-05-18T04:15:49.392101+00:00"},{"alias_kind":"pith_short_12","alias_value":"YGRZP4Z474UP","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YGRZP4Z474UPR2DE","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YGRZP4Z4","created_at":"2026-05-18T12:26:47.523578+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/YGRZP4Z474UPR2DEBRT5BPPKRM","json":"https://pith.science/pith/YGRZP4Z474UPR2DEBRT5BPPKRM.json","graph_json":"https://pith.science/api/pith-number/YGRZP4Z474UPR2DEBRT5BPPKRM/graph.json","events_json":"https://pith.science/api/pith-number/YGRZP4Z474UPR2DEBRT5BPPKRM/events.json","paper":"https://pith.science/paper/YGRZP4Z4"},"agent_actions":{"view_html":"https://pith.science/pith/YGRZP4Z474UPR2DEBRT5BPPKRM","download_json":"https://pith.science/pith/YGRZP4Z474UPR2DEBRT5BPPKRM.json","view_paper":"https://pith.science/paper/YGRZP4Z4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2083&json=true","fetch_graph":"https://pith.science/api/pith-number/YGRZP4Z474UPR2DEBRT5BPPKRM/graph.json","fetch_events":"https://pith.science/api/pith-number/YGRZP4Z474UPR2DEBRT5BPPKRM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YGRZP4Z474UPR2DEBRT5BPPKRM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YGRZP4Z474UPR2DEBRT5BPPKRM/action/storage_attestation","attest_author":"https://pith.science/pith/YGRZP4Z474UPR2DEBRT5BPPKRM/action/author_attestation","sign_citation":"https://pith.science/pith/YGRZP4Z474UPR2DEBRT5BPPKRM/action/citation_signature","submit_replication":"https://pith.science/pith/YGRZP4Z474UPR2DEBRT5BPPKRM/action/replication_record"}},"created_at":"2026-05-18T04:15:49.392101+00:00","updated_at":"2026-05-18T04:15:49.392101+00:00"}