{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5PQJ3HJ73Z7WYM2HWUXYBZTQLF","short_pith_number":"pith:5PQJ3HJ7","schema_version":"1.0","canonical_sha256":"ebe09d9d3fde7f6c3347b52f80e6705965ca96f572a39b596f7b6a006dba9921","source":{"kind":"arxiv","id":"1609.02798","version":2},"attestation_state":"computed","paper":{"title":"Pseudo core inverses in rings with involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jianlong Chen, Yuefeng Gao","submitted_at":"2016-09-09T14:02:59Z","abstract_excerpt":"Let $R$ be a ring with involution. In this paper, we introduce a new type of generalized inverse called pseudo core inverse in $R$. The notion of core inverse was introduced by Baksalary and Trenkler for matrices of index 1 in 2010 and then it was generalized to an arbitrary $*$-ring case by Raki\\'{c}, Din\\v{c}i\\'{c} and Djordjevi\\'{c} in 2014. Our definition of pesudo core inverse extends the notion of core inverse to elements of an arbitrary index in $R$. Meanwhile, it generalizes the notion of core-EP inverse, introduced by Manjunatha Prasad and Mohana for matrices in 2014, to the case of $"},"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":"1609.02798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-09T14:02:59Z","cross_cats_sorted":[],"title_canon_sha256":"32ba502d5a5d5494ec32e35e5d1b89f5f6d964c3db93904f0056a9736c89cd12","abstract_canon_sha256":"e6f1ea42e15cabb1cedd12d26f7d20bfb672b96665fe45ff0b20f3e1a2b61e22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:39.880009Z","signature_b64":"0Dbeqh3dGPWj50bMvMSs5tCNzHr6EeyEwns1F0JFQV0joobfmHWc4Sjr1FBDj3g3ZJF4TzJyoGsmnLN9lHDYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebe09d9d3fde7f6c3347b52f80e6705965ca96f572a39b596f7b6a006dba9921","last_reissued_at":"2026-05-18T00:46:39.879292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:39.879292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudo core inverses in rings with involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jianlong Chen, Yuefeng Gao","submitted_at":"2016-09-09T14:02:59Z","abstract_excerpt":"Let $R$ be a ring with involution. In this paper, we introduce a new type of generalized inverse called pseudo core inverse in $R$. The notion of core inverse was introduced by Baksalary and Trenkler for matrices of index 1 in 2010 and then it was generalized to an arbitrary $*$-ring case by Raki\\'{c}, Din\\v{c}i\\'{c} and Djordjevi\\'{c} in 2014. Our definition of pesudo core inverse extends the notion of core inverse to elements of an arbitrary index in $R$. Meanwhile, it generalizes the notion of core-EP inverse, introduced by Manjunatha Prasad and Mohana for matrices in 2014, to the case of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02798","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":"1609.02798","created_at":"2026-05-18T00:46:39.879424+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.02798v2","created_at":"2026-05-18T00:46:39.879424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02798","created_at":"2026-05-18T00:46:39.879424+00:00"},{"alias_kind":"pith_short_12","alias_value":"5PQJ3HJ73Z7W","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5PQJ3HJ73Z7WYM2H","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5PQJ3HJ7","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/5PQJ3HJ73Z7WYM2HWUXYBZTQLF","json":"https://pith.science/pith/5PQJ3HJ73Z7WYM2HWUXYBZTQLF.json","graph_json":"https://pith.science/api/pith-number/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/graph.json","events_json":"https://pith.science/api/pith-number/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/events.json","paper":"https://pith.science/paper/5PQJ3HJ7"},"agent_actions":{"view_html":"https://pith.science/pith/5PQJ3HJ73Z7WYM2HWUXYBZTQLF","download_json":"https://pith.science/pith/5PQJ3HJ73Z7WYM2HWUXYBZTQLF.json","view_paper":"https://pith.science/paper/5PQJ3HJ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.02798&json=true","fetch_graph":"https://pith.science/api/pith-number/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/graph.json","fetch_events":"https://pith.science/api/pith-number/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/action/storage_attestation","attest_author":"https://pith.science/pith/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/action/author_attestation","sign_citation":"https://pith.science/pith/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/action/citation_signature","submit_replication":"https://pith.science/pith/5PQJ3HJ73Z7WYM2HWUXYBZTQLF/action/replication_record"}},"created_at":"2026-05-18T00:46:39.879424+00:00","updated_at":"2026-05-18T00:46:39.879424+00:00"}