{"paper":{"title":"Dyadic Steenrod algebra and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ali S. Janfada, Ghorban Soleymanpour","submitted_at":"2017-09-20T16:54:22Z","abstract_excerpt":"First, by inspiration of the results of Wood \\cite{differential,problems}, but with the methods of non-commutative geometry and different approach, we extend the coefficients of the Steenrod squaring operations from the filed $\\mathbb{F}_2$ to the dyadic integers $\\mathbb{Z}_2$ and call the resulted operations the dyadic Steenrod squares, denoted by $Jq^k$. The derivation-like operations $Jq^k$ generate a graded algebra, called the dyadic Steenrod algebra, denoted by $\\mathcal{J}_2$ acting on the polynomials $\\mathbb{Z}_2[\\xi_1, \\dots, \\xi_n]$. Being $\\mathcal{J}_2$ an Ore domain, enable us to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06962","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"}