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Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(K) can be constructed by a polynomial time ff-algorithm. (An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.)\n  As a consequence, we obtain a polynomial time ff-algorithm to com"},"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":"1106.6191","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:27:48Z","cross_cats_sorted":["cs.SC","math.NT"],"title_canon_sha256":"2ac5154d2852fea5adf0b9285c22fda988028298b7c3c4c255261d49e05e715a","abstract_canon_sha256":"d29899e61c71908771820453b78a0d0d6a7a76197ceb8f36ebfbc0d4ca8f721b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:57.610557Z","signature_b64":"F6TjVdCDTU+CU+0Ld7M/glY6KvM42aZ7LlciHkTWz6asFH0ImW7oPDes30Bo594rBvA6u0qDOZ85P2EOy5BpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe228003f1a80850ad6d1057bd6a52a4bbbf299ce8b775e1253df18f3b196b31","last_reissued_at":"2026-05-18T04:05:57.609999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:57.609999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Splitting full matrix algebras over algebraic number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NT"],"primary_cat":"math.RA","authors_text":"G\\'abor Ivanyos, Josef Schicho, Lajos R\\'onyai","submitted_at":"2011-06-30T11:27:48Z","abstract_excerpt":"Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(K) can be constructed by a polynomial time ff-algorithm. 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