{"paper":{"title":"Complementation in the Group of Units of Matrix Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Stewart Wilcox","submitted_at":"2010-10-07T04:29:47Z","abstract_excerpt":"Let $R$ be a ring with $1$ and $\\J(R)$ its Jacobson radical. Then $1+\\J(R)$ is a normal subgroup of the group of units, $G(R)$. The existence of a complement to this subgroup was explored in a paper by Coleman and Easdown; in particular the ring $R=\\Mat_n(\\Z_{p^k})$ was considered. We prove the remaining cases to determine for which $n$, $p$ and $k$ a complement exists in this ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1332","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"}