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More precisely, if S denotes all non-zero degree e central elements of W, the algebra S^{-1}W is G-graded simple and finite dimensional over its center.\n  Furthermore, we show how to use this theorem in order to recapture the result of Aljadeff and Haile stating that two G-simple algebras of finite dimension are isomorphix iff their ideals of graded identities coincide."},"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":"1610.03977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-13T08:37:17Z","cross_cats_sorted":[],"title_canon_sha256":"54eea83a60159d9c2b02854e14e0fd74f71338c8c7543e9c3c7817e678db272a","abstract_canon_sha256":"75dbd9a2433985d7062b65d32ca2971d7c7821f872ab4adf1eca91f751b9e0be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:22.821225Z","signature_b64":"1veVbfhb+0j/G90+y0ovIhZBhsyp1Y9ZJJTLX03EHbHpnxOZKA+shPsKWVExMFZ7SzkkANT0rUaS4AOx3X8bDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46bfb8c430ea8924b0843f5d7b58037cc6b59be04a59c6ed5af0b0b82f362746","last_reissued_at":"2026-05-18T01:02:22.820581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:22.820581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"G-Graded Central Polynomials and G-Graded Posner's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Yakov Karasik","submitted_at":"2016-10-13T08:37:17Z","abstract_excerpt":"Let F be characteristic zero field, G a residually finite group and W a G-prime and PI F-algebra. 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