{"paper":{"title":"Modules of covariants in modular invariant theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Abraham Broer, Jianjun Chuai","submitted_at":"2007-09-05T16:47:14Z","abstract_excerpt":"Let the finite group $G$ act linearly on the vector space $V$ over the field $k$ of arbitrary characteristic. If $H<G$ is a subgroup the extension of invariant rings $k[V]^G\\subset k[V]^H$ is studied using modules of covariants.\n  An example of our results is the following. Let $W$ be the subgroup of $G$ generated by the reflections in $G$. A classical theorem due to Serre says that if $k[V]$ is a free $k[V]^G$-module then $G=W$. We generalize this result as follows. If $k[V]^H$ is a free $k[V]^G$-module then $G$ is generated by $H$ and $W$, and the invariant ring $k[V]^{H\\cap W}$ is free over"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0703","kind":"arxiv","version":3},"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"}