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We study the ideal $I_f$ of $R[X_1,\\dots,X_n]$ generated by $\\sigma_i(X_1,\\dots,X_n)-a_{i}$, where $\\sigma_1,\\dots,\\sigma_n$ are the elementary symmetric polynomials, as well as the quotient ring $R[X_1,\\dots,X_n]/I_f$."},"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":"1504.00973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-04-04T02:46:05Z","cross_cats_sorted":[],"title_canon_sha256":"2475afe2199d1f42017db865337c5cf04a11b60ac4ee3581ac617327e3e3f58a","abstract_canon_sha256":"f0ebba02fe577dc8965f3b3263bfe9c089b0b44ca495039404663e096bf6ea70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:01.057195Z","signature_b64":"elypW6TMBekxFS33w3X4FBuZOBlkY/ruuDbArJ+lbS4n/Tt+TxSe2gvnWFtFnzZtqUIhrqm18raQ0XHcyjgzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e652ae93914f77cc46e8a692c04f0622e5a8af3193955e932c62482a59f24e67","last_reissued_at":"2026-05-18T01:30:01.056749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:01.056749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the splitting ring of a polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fernando Szechtman","submitted_at":"2015-04-04T02:46:05Z","abstract_excerpt":"Let $f(Z)=Z^n-a_{1}Z^{n-1}+\\cdots+(-1)^{n-1}a_{n-1}Z+(-1)^na_n$ be a monic polynomial with coefficients in a ring~$R$ with identity, not necessarily commutative. We study the ideal $I_f$ of $R[X_1,\\dots,X_n]$ generated by $\\sigma_i(X_1,\\dots,X_n)-a_{i}$, where $\\sigma_1,\\dots,\\sigma_n$ are the elementary symmetric polynomials, as well as the quotient ring $R[X_1,\\dots,X_n]/I_f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00973","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":"1504.00973","created_at":"2026-05-18T01:30:01.056812+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.00973v2","created_at":"2026-05-18T01:30:01.056812+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00973","created_at":"2026-05-18T01:30:01.056812+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ZJK5E4RJ534","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ZJK5E4RJ534YRXI","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ZJK5E4R","created_at":"2026-05-18T12:29:05.191682+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/4ZJK5E4RJ534YRXIU2JMATYGEL","json":"https://pith.science/pith/4ZJK5E4RJ534YRXIU2JMATYGEL.json","graph_json":"https://pith.science/api/pith-number/4ZJK5E4RJ534YRXIU2JMATYGEL/graph.json","events_json":"https://pith.science/api/pith-number/4ZJK5E4RJ534YRXIU2JMATYGEL/events.json","paper":"https://pith.science/paper/4ZJK5E4R"},"agent_actions":{"view_html":"https://pith.science/pith/4ZJK5E4RJ534YRXIU2JMATYGEL","download_json":"https://pith.science/pith/4ZJK5E4RJ534YRXIU2JMATYGEL.json","view_paper":"https://pith.science/paper/4ZJK5E4R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.00973&json=true","fetch_graph":"https://pith.science/api/pith-number/4ZJK5E4RJ534YRXIU2JMATYGEL/graph.json","fetch_events":"https://pith.science/api/pith-number/4ZJK5E4RJ534YRXIU2JMATYGEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ZJK5E4RJ534YRXIU2JMATYGEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ZJK5E4RJ534YRXIU2JMATYGEL/action/storage_attestation","attest_author":"https://pith.science/pith/4ZJK5E4RJ534YRXIU2JMATYGEL/action/author_attestation","sign_citation":"https://pith.science/pith/4ZJK5E4RJ534YRXIU2JMATYGEL/action/citation_signature","submit_replication":"https://pith.science/pith/4ZJK5E4RJ534YRXIU2JMATYGEL/action/replication_record"}},"created_at":"2026-05-18T01:30:01.056812+00:00","updated_at":"2026-05-18T01:30:01.056812+00:00"}