{"paper":{"title":"The graded algebra of Steenrod $q$th powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Grant Walker","submitted_at":"2018-12-18T14:43:18Z","abstract_excerpt":"The algebra ${\\mathsf A}_q$ of Steenrod $q$th powers, where $q = p^e$ is a power of a prime $p$, is isomorphic to a subalgebra ${\\mathsf A}'_q$ of the algebra of Steenrod $p$th powers ${\\mathsf A}_p$. The filtration of ${\\mathsf A}_p$ by powers of its augmentation ideal was studied by J. P. May in his Princeton thesis of 1964. We extend some of May's results to ${\\mathsf A}_q$ and obtain a convenient set of defining relations for the graded algebra $E^0({\\mathsf A}_q)$. In the case $q=p$, we recover the observation of S. B. Priddy that the subalgebra $E^0({\\mathsf A}_p(n-2))$ of $E^0({\\mathsf "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07395","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}