{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MOHHQRH7577UWGKDEVTSKBWBPL","short_pith_number":"pith:MOHHQRH7","canonical_record":{"source":{"id":"1701.07117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-25T00:41:58Z","cross_cats_sorted":[],"title_canon_sha256":"b44b72154541e009ed8b44bc8fca2a69ca5de38c6538a1a6bbef08abaa0087f4","abstract_canon_sha256":"786afa03e3f2940ae112362a6ae625a5c9944e8df029fee33a9bd71e6d75fc4e"},"schema_version":"1.0"},"canonical_sha256":"638e7844ffefff4b194325672506c17acce1f6e239fde9a3b5274dfd4ed9be5e","source":{"kind":"arxiv","id":"1701.07117","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07117","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07117v1","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07117","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"MOHHQRH7577U","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MOHHQRH7577UWGKD","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MOHHQRH7","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MOHHQRH7577UWGKDEVTSKBWBPL","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-25T00:41:58Z","cross_cats_sorted":[],"title_canon_sha256":"b44b72154541e009ed8b44bc8fca2a69ca5de38c6538a1a6bbef08abaa0087f4","abstract_canon_sha256":"786afa03e3f2940ae112362a6ae625a5c9944e8df029fee33a9bd71e6d75fc4e"},"schema_version":"1.0"},"canonical_sha256":"638e7844ffefff4b194325672506c17acce1f6e239fde9a3b5274dfd4ed9be5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:29.354063Z","signature_b64":"axaAGmMWPR8BRbRHbdQpOPKR8WfjE4R3z9PHHulH91LiFc86SlCOMuONy7yV5Vap6nI3oNzMUEW7QT00rtOuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"638e7844ffefff4b194325672506c17acce1f6e239fde9a3b5274dfd4ed9be5e","last_reissued_at":"2026-05-18T00:48:29.353583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:29.353583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07117","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tH8wTG0SdZnBRtHHkOf3bplP8acn8OT6sLj4KQknuxY696Ro0AhV4TP58vTKsEMWKKDLgh1NRdPQaz7zPmNUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:07:58.404182Z"},"content_sha256":"12c5931171e6d5066f22056e0973566b84c30449150e1ee1e1d06cbb2345fd53","schema_version":"1.0","event_id":"sha256:12c5931171e6d5066f22056e0973566b84c30449150e1ee1e1d06cbb2345fd53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MOHHQRH7577UWGKDEVTSKBWBPL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modules over strongly semiprime ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Askar Tuganbaev","submitted_at":"2017-01-25T00:41:58Z","abstract_excerpt":"$\\textbf{Theorem 1.3.}$ For a given ring $A$ with right Goldie radical $G(A_A)$, the following conditions are equivalent. $\\textbf{1)}$ Every non-singular right $A$-module $X$ which is is injective with respect to some essential right ideal of the ring $A$ is an injective module. $\\textbf{2)}$ $A/G(A_A)$ is a right strongly semiprime ring. $\\textbf{Theorem 1.4.}$ For a given ring $A$, the following conditions are equivalent. $\\textbf{1)}$ $A$ is a right strongly semiprime ring. $\\textbf{2)}$ Every right $A$-module which is injective with respect to some essential right ideal of the ring $A$, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07117","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KQ87OtKk5z6jB0J47qvFfhrtd/f+LQcZKErV9HoOO4Ug4J08zbrRyfMM7S5z0xMzLFMN6yLaUa0xhizkjvX2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:07:58.404557Z"},"content_sha256":"80c18a1ba4ecadbd4b2783d79d8680439feb9030a11bc82e2b3975d29a2cd320","schema_version":"1.0","event_id":"sha256:80c18a1ba4ecadbd4b2783d79d8680439feb9030a11bc82e2b3975d29a2cd320"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MOHHQRH7577UWGKDEVTSKBWBPL/bundle.json","state_url":"https://pith.science/pith/MOHHQRH7577UWGKDEVTSKBWBPL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MOHHQRH7577UWGKDEVTSKBWBPL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T01:07:58Z","links":{"resolver":"https://pith.science/pith/MOHHQRH7577UWGKDEVTSKBWBPL","bundle":"https://pith.science/pith/MOHHQRH7577UWGKDEVTSKBWBPL/bundle.json","state":"https://pith.science/pith/MOHHQRH7577UWGKDEVTSKBWBPL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MOHHQRH7577UWGKDEVTSKBWBPL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MOHHQRH7577UWGKDEVTSKBWBPL","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":"786afa03e3f2940ae112362a6ae625a5c9944e8df029fee33a9bd71e6d75fc4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-25T00:41:58Z","title_canon_sha256":"b44b72154541e009ed8b44bc8fca2a69ca5de38c6538a1a6bbef08abaa0087f4"},"schema_version":"1.0","source":{"id":"1701.07117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07117","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07117v1","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07117","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"MOHHQRH7577U","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MOHHQRH7577UWGKD","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MOHHQRH7","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:80c18a1ba4ecadbd4b2783d79d8680439feb9030a11bc82e2b3975d29a2cd320","target":"graph","created_at":"2026-05-18T00:48:29Z","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":"$\\textbf{Theorem 1.3.}$ For a given ring $A$ with right Goldie radical $G(A_A)$, the following conditions are equivalent. $\\textbf{1)}$ Every non-singular right $A$-module $X$ which is is injective with respect to some essential right ideal of the ring $A$ is an injective module. $\\textbf{2)}$ $A/G(A_A)$ is a right strongly semiprime ring. $\\textbf{Theorem 1.4.}$ For a given ring $A$, the following conditions are equivalent. $\\textbf{1)}$ $A$ is a right strongly semiprime ring. $\\textbf{2)}$ Every right $A$-module which is injective with respect to some essential right ideal of the ring $A$, i","authors_text":"Askar Tuganbaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-25T00:41:58Z","title":"Modules over strongly semiprime ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07117","kind":"arxiv","version":1},"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":"sha256:12c5931171e6d5066f22056e0973566b84c30449150e1ee1e1d06cbb2345fd53","target":"record","created_at":"2026-05-18T00:48:29Z","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":"786afa03e3f2940ae112362a6ae625a5c9944e8df029fee33a9bd71e6d75fc4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-25T00:41:58Z","title_canon_sha256":"b44b72154541e009ed8b44bc8fca2a69ca5de38c6538a1a6bbef08abaa0087f4"},"schema_version":"1.0","source":{"id":"1701.07117","kind":"arxiv","version":1}},"canonical_sha256":"638e7844ffefff4b194325672506c17acce1f6e239fde9a3b5274dfd4ed9be5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"638e7844ffefff4b194325672506c17acce1f6e239fde9a3b5274dfd4ed9be5e","first_computed_at":"2026-05-18T00:48:29.353583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:29.353583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"axaAGmMWPR8BRbRHbdQpOPKR8WfjE4R3z9PHHulH91LiFc86SlCOMuONy7yV5Vap6nI3oNzMUEW7QT00rtOuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:29.354063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12c5931171e6d5066f22056e0973566b84c30449150e1ee1e1d06cbb2345fd53","sha256:80c18a1ba4ecadbd4b2783d79d8680439feb9030a11bc82e2b3975d29a2cd320"],"state_sha256":"888eb0ee8e93338c9564c34b4c9ad3b25b98659c9be8cf1615c3f26e8275187b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ngx3mZcqtc3hN5XoB6oaFmBi+mTflEA2qHGkfD3OSJIoCiZKJQioyF6uFxb+ST9bTb8hy4ihaiKESKGjp2bSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:07:58.406598Z","bundle_sha256":"2a9f02c7b9b519fd1f708586ad1f94b8b3428a6fad1d82b8b129dfedc06a4cee"}}