{"paper":{"title":"Torsion Freeness of Schur Modules","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alexandre Tchernev, Muberra Allahverdi","submitted_at":"2018-08-02T00:01:50Z","abstract_excerpt":"Let $R$ be a Noetherian commutative ring and $M$ an $R$-module with $\\operatorname{pd_R} M\\le 1$ that has rank. Necessary and sufficient conditions were provided by Lebelt for an exterior power $\\wedge^k M$ to be torsion free. When $M$ is an ideal of $R$ similar necessary and sufficient conditions were provided by Tchernev for a symmetric power $S_k M$ to be torsion free. We extend these results to a broad class of Schur modules $L_{\\lambda/\\mu} M$. En route, for any map of finite free $R$ modules $\\phi\\: F\\rightarrow G$ we also study the general structure of the Schur complexes $L_{\\lambda/\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00602","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"}