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For that Hopf Galois structure we may study the image of the Galois correspondence from $k$-subHopf algebras of $H$ to subfields of $K$ containing $k$ by utilizing the fact that the intermediate subfields correspond to the $\\mathbb{F}_p$-subspaces of $A$, while the subHopf algebras of $H$ correspond to the ideals "},"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":"1706.02518","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-08T11:22:46Z","cross_cats_sorted":[],"title_canon_sha256":"dbab66dea7aa9bec21c1a73b9d959598c2a194998e23e66089a1cb65bb481ec6","abstract_canon_sha256":"825f92379dc08491e452ec1836815be481aa2dd48753d30663fb489c9df8ab42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:45.237003Z","signature_b64":"e+r0jQBaS0TCWOpEGuPwZnCB+wwpJklv8+Saqvzky8EqMCrOymCIZdykPTdn7XjkFZWcoPR3R/kCFSNOqs1OBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffcdad1d15faa901d86a3b2fad1b4c18176d99af3916ce177418ae8bf44dbc42","last_reissued_at":"2026-05-18T00:42:45.236589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:45.236589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on the number of ideals in finite commutative nilpotent $\\mathbb{F}_p$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Cornelius Greither, Lindsay N. 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