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The dual problem is to determine the set of $\\mathcal {A}$-annihilated elements in homology. The set of $\\mathcal{A}$-annihilateds has been shown by David Anick to be a free associative algebra. In this note we prove that, for each $k \\geq 0$, the set of {\\it $k$ partially $\\mathcal{A}$-annihilateds}, the set of elements that are annihilated by $Sq^i"},"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":"1105.1139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-05T18:27:49Z","cross_cats_sorted":[],"title_canon_sha256":"b4a95c7785c6f0c29f15a671f6bfe30dd524546bc0787b63df3aa143bf2f2c11","abstract_canon_sha256":"4f9cecd41b07e6e2f8f23b8fda740e94a8ee29761c49ed2f0960b71ea68108ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:10.242563Z","signature_b64":"bmTpumhwq5hA+rPKZDJzyGQ6ueJpBlG1gDGFGpe0sU8YzSw6hau54m0ROXDDt+sSiwuOQuNUwvggy1+IyOtVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f29d99d810886416152037d989716d90b0c7d7cc51296e4427bfd691d6af5604","last_reissued_at":"2026-05-18T02:48:10.241835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:10.241835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Homology of Elementary Abelian Groups as Modules over the Steenrod Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Shaun V. 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