{"paper":{"title":"Writing units of integral group rings of finite abelian groups as a product of Bass units","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"\\'Angel del R\\'io, Eric Jespers, Inneke Van Gelder","submitted_at":"2011-11-15T10:15:36Z","abstract_excerpt":"We give a constructive proof of the theorem of Bass and Milnor saying that if $G$ is a finite abelian group then the Bass units of the integral group ring $\\Z G$ generate a subgroup of finite index in its units group $\\U(\\Z G)$. Our proof provides algorithms to represent some units that contribute to only one simple component of $\\Q G$ and generate a subgroup of finite index in $\\U(\\Z G)$ as product of Bass units. We also obtain a basis $B$ formed by Bass units of a free abelian subgroup of finite index in $\\U(\\Z G)$ and give, for an arbitrary Bass unit $b$, an algorithm to express $b^{\\varphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3485","kind":"arxiv","version":2},"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"}