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Using this construction, we prove a common connection between the semigroups $S$, $S/\\theta$ and $S/\\theta ^*=(S/\\theta)/(\\theta ^*/\\theta)$, where $\\theta$ and $\\theta ^*/\\theta$ are the kernels of the right regular representations of $S$ and $S/\\theta$, respectively. We also prove an embedding theorem for the sem"},"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":"1510.05291","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-18T18:21:03Z","cross_cats_sorted":[],"title_canon_sha256":"fea713a56c3c1f82e882e37b317018395101bdb3cf20d0ec347fa57bba2d7c96","abstract_canon_sha256":"703bd0ecdf76d0a22b440e3b7e72879dabfe960f66f6ed3807af117b912b1af8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:52.655909Z","signature_b64":"dAXRw60bxIbUf8mXoE+8gehzcxioqjIE4USjz/Y4govflfyu2rrrK0nGA4QRTwu8zjmrfUyYw6Hx25UFxmZhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b93625211293fedefc5e0c37338bd1b5d3efdff173ade62cf03c00a3c11cff94","last_reissued_at":"2026-05-18T01:29:52.655290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:52.655290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Special Semigroups Derived From an Arbitrary Semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Attila Nagy","submitted_at":"2015-10-18T18:21:03Z","abstract_excerpt":"Let $S$ be a semigroup, $\\Lambda$ a non-empty set and $P$ a mapping of $\\Lambda$ into $S$. The set $S\\times \\Lambda$ together with the operation $\\circ _P$ defined by $(s, \\lambda)\\circ _P(t, \\mu )=(sP(\\lambda)t, \\mu )$ form a semigroup which is denoted by $(S, \\Lambda , \\circ _P)$. Using this construction, we prove a common connection between the semigroups $S$, $S/\\theta$ and $S/\\theta ^*=(S/\\theta)/(\\theta ^*/\\theta)$, where $\\theta$ and $\\theta ^*/\\theta$ are the kernels of the right regular representations of $S$ and $S/\\theta$, respectively. We also prove an embedding theorem for the sem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05291","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":"1510.05291","created_at":"2026-05-18T01:29:52.655388+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.05291v1","created_at":"2026-05-18T01:29:52.655388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05291","created_at":"2026-05-18T01:29:52.655388+00:00"},{"alias_kind":"pith_short_12","alias_value":"XE3CKIISSP7N","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XE3CKIISSP7N57C6","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XE3CKIIS","created_at":"2026-05-18T12:29:50.041715+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/XE3CKIISSP7N57C6BQ3THC6RWX","json":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX.json","graph_json":"https://pith.science/api/pith-number/XE3CKIISSP7N57C6BQ3THC6RWX/graph.json","events_json":"https://pith.science/api/pith-number/XE3CKIISSP7N57C6BQ3THC6RWX/events.json","paper":"https://pith.science/paper/XE3CKIIS"},"agent_actions":{"view_html":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX","download_json":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX.json","view_paper":"https://pith.science/paper/XE3CKIIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.05291&json=true","fetch_graph":"https://pith.science/api/pith-number/XE3CKIISSP7N57C6BQ3THC6RWX/graph.json","fetch_events":"https://pith.science/api/pith-number/XE3CKIISSP7N57C6BQ3THC6RWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/action/storage_attestation","attest_author":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/action/author_attestation","sign_citation":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/action/citation_signature","submit_replication":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/action/replication_record"}},"created_at":"2026-05-18T01:29:52.655388+00:00","updated_at":"2026-05-18T01:29:52.655388+00:00"}