{"paper":{"title":"Semigroups of rectangular matrices under a sandwich operation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Igor Dolinka, James East","submitted_at":"2015-03-11T01:04:25Z","abstract_excerpt":"Let $\\mathcal M_{mn}=\\mathcal M_{mn}(\\mathbb F)$ denote the set of all $m\\times n$ matrices over a field $\\mathbb F$, and fix some $n\\times m$ matrix $A\\in\\mathcal M_{nm}$. An associative operation $\\star$ may be defined on $\\mathcal M_{mn}$ by $X\\star Y=XAY$ for all $X,Y\\in\\mathcal M_{mn}$, and the resulting \\emph{sandwich semigroup} is denoted $\\mathcal M_{mn}^A=\\mathcal M_{mn}^A(\\mathbb F)$. These semigroups are closely related to Munn rings, which are fundamental tools in the representation theory of finite semigroups. In this article, we study $\\mathcal M_{mn}^A$ as well as its subsemigro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03139","kind":"arxiv","version":2},"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"}