{"paper":{"title":"On generating the ring of matrix semi-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RA"],"primary_cat":"cs.CC","authors_text":"G\\'abor Ivanyos, K. V. Subrahmanyam, Youming Qiao","submitted_at":"2015-08-06T22:20:57Z","abstract_excerpt":"For a field $\\mathbb{F}$, let $R(n, m)$ be the ring of invariant polynomials for the action of $\\mathrm{SL}(n, \\mathbb{F}) \\times \\mathrm{SL}(n, \\mathbb{F})$ on tuples of matrices -- $(A, C)\\in\\mathrm{SL}(n, \\mathbb{F}) \\times \\mathrm{SL}(n, \\mathbb{F})$ sends $(B_1, \\dots, B_m)\\in M(n, \\mathbb{F})^{\\oplus m}$ to $(AB_1C^{-1}, \\dots, AB_mC^{-1})$. In this paper we call $R(n, m)$ the \\emph{ring of matrix semi-invariants}. Let $\\beta(R(n, m))$ be the smallest $D$ s.t. matrix semi-invariants of degree $\\leq D$ generate $R(n, m)$. Guided by the Procesi-Razmyslov-Formanek approach of proving a stro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01554","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"}