{"paper":{"title":"On modules of linear transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bamdad R. Yahaghi, M. Rahimi-Alangi","submitted_at":"2015-08-01T04:12:04Z","abstract_excerpt":"Let $D$ be a division ring, $\\mathcal V$ and $ \\mathcal W$ vector spaces over $D$, and ${\\mathcal L(\\mathcal V,\\mathcal W)}$ the ${\\mathcal L(\\mathcal W)}$-${\\mathcal L(\\mathcal V)}$ bimodule of all linear transformations from $\\mathcal V$ into $\\mathcal W$. We prove some basic results about certain submodules of $\\mathcal L(\\mathcal V, \\mathcal W)$. For instance, we show, among other results, that a right submodule (resp. left submodule) of ${\\mathcal L(\\mathcal V,\\mathcal W)}$ is finitely generated whenever its image (resp. coimage) is finite-dimensional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00072","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"}