{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:W2NKPHJYF5CEQVPXHAEACAJAPU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"826bb35fe7b0a596fda6b8ea8c29cab9a5230582c17304c5fdba311ea94505c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-03T10:27:09Z","title_canon_sha256":"be09d57f4144644b805e44d011ca96f6f4385ab2efd2b320ed7101b1eb4ea077"},"schema_version":"1.0","source":{"id":"1701.00621","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00621","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00621v2","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00621","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"pith_short_12","alias_value":"W2NKPHJYF5CE","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"W2NKPHJYF5CEQVPX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"W2NKPHJY","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:eaca1226983565bb955b6237430b21e26e97ebaf51ca76d0e42bd6d68d9f436e","target":"graph","created_at":"2026-05-18T00:46:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we investigate *-DMP elements in $*$-semigroups and $*$-rings. The notion of *-DMP element was introduced by Patr\\'{i}cio in 2004. An element $a$ is *-DMP if there exists a positive integer $m$ such that $a^{m}$ is EP. We first characterize *-DMP elements in terms of the \\{1,3\\}-inverse, Drazin inverse and pseudo core inverse, respectively.\n  Then, we give the pseudo core decomposition utilizing the pseudo core inverse, which extends the core-EP decomposition introduced by Wang for matrices to an arbitrary $*$-ring; and this decomposition turns to be a useful tool to characteriz","authors_text":"Jianlong Chen, Yuanyuan Ke, Yuefeng Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-03T10:27:09Z","title":"*-DMP elements in $*$-semigroups and $*$-rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00621","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e8ecb15b4249182cddcf2ceaa543d5a846a5df746730c36ebd4bc3c7a5c60823","target":"record","created_at":"2026-05-18T00:46:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"826bb35fe7b0a596fda6b8ea8c29cab9a5230582c17304c5fdba311ea94505c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-03T10:27:09Z","title_canon_sha256":"be09d57f4144644b805e44d011ca96f6f4385ab2efd2b320ed7101b1eb4ea077"},"schema_version":"1.0","source":{"id":"1701.00621","kind":"arxiv","version":2}},"canonical_sha256":"b69aa79d382f444855f738080101207d18393fcb94cddfbdb2e9b25c6d8b2468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b69aa79d382f444855f738080101207d18393fcb94cddfbdb2e9b25c6d8b2468","first_computed_at":"2026-05-18T00:46:38.197687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:38.197687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a1CDNeS5Z7TXGmu+4bmRdEbVYJIY9x1GP8f3OgaddLCXZayRHkbMn+DBbFWZab7biEAUmuxR+l3cyp1/fqxVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:38.198279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00621","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8ecb15b4249182cddcf2ceaa543d5a846a5df746730c36ebd4bc3c7a5c60823","sha256:eaca1226983565bb955b6237430b21e26e97ebaf51ca76d0e42bd6d68d9f436e"],"state_sha256":"3b25e962322530d8ee43213cf1d83ea1180086dfb882c66396e94babfeeb906f"}