{"paper":{"title":"Formal Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jos\\'e Carrasco, Piergiulio Tempesta","submitted_at":"2019-02-10T20:27:32Z","abstract_excerpt":"A notion of one-dimensional formal ring is presented. It consists of a triple $(A,\\Phi,\\Psi)$ where $A$ is a unital ring and $\\Phi$ and $\\Psi$ are two formal power series in $2$ variables ${\\Phi(x,y),\\Psi(x,y)\\in A\\llbracket x,y\\rrbracket}$, the first one defining a one-dimensional formal group law over $A$ and the second one providing a second composition law satisfying axiomatic properties of compatibility with the first one. For a characteristic-zero ring $A$, a large class of one-dimensional formal rings can be obtained by constructing a new composition law, defined in terms of the group l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03665","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"}