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If G is abelian and A is commutative, then $A \\rtimes_{\\sigma} G$ is shown to be simple if and only if \\sigma is injective and A is G-simple. As an application we show that a transformation group (X,G), where X is a compact Hausdorff space and G is abelian, is minimal and faithful if and only if its associa"},"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":"1111.7214","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-11-30T15:40:29Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"71d9bba77152238388d21f0860725d2df1fe1f0c7abff735e6c807d6c60eb03a","abstract_canon_sha256":"a79dc683321f695bc7b69dc377bcb379270a71b536bdd866e11562063c2be2f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:06.646742Z","signature_b64":"/l3qPCMtef1qTwc0QrFC8gjb1kcpXgYRi/bjRCeUp43P77AT+x73Zu1PsLmJA4+6dB5G77hCXwaBPh7NSAoeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"251cf43fc28831c12146e470bcae2ce5c40ed640602186e8f71037be438b838e","last_reissued_at":"2026-05-18T02:59:06.645856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:06.645856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simplicity of skew group rings of abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert","submitted_at":"2011-11-30T15:40:29Z","abstract_excerpt":"Given a group G, a (unital) ring A and a group homomorphism $\\sigma : G \\to \\Aut(A)$, one can construct the skew group ring $A \\rtimes_{\\sigma} G$. 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