{"paper":{"title":"An alternative look at the structure of graph inverse semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Serhii Bardyla","submitted_at":"2018-06-25T19:18:01Z","abstract_excerpt":"For any graph inverse semigroup $G(E)$ we describe subsemigroups $D^0=D\\cup\\{0\\}$ and $J^0=J\\cup\\{0\\}$ of $G(E)$ where $D$ and $J$ are arbitrary $\\mathcal{D}$-class and $\\mathcal{J}$-class of $G(E)$, respectively. In particular, we prove that for each $\\mathcal{D}$-class $D$ of a graph inverse semigroup over an acyclic graph the semigroup $D^0$ is isomorphic to a semigroup of matrix units. Also we show that for any elements $a,b$ of a graph inverse semigroup $G(E)$, $J_a\\cdot J_b\\cup J_b\\cdot J_a\\subset J_b^0$ if there exists a path $w$ such that $s(w)\\in J_a$ and $r(w)\\in J_b$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09671","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"}