{"paper":{"title":"A Note on Semigroup Algebras of Permutable Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Attila Nagy, M\\'arton Zubor","submitted_at":"2015-11-27T13:44:47Z","abstract_excerpt":"Let $S$ be a semigroup and $\\mathbb F$ be a field. For an ideal $J$ of the semigroup algebra ${\\mathbb F}[S]$ of $S$ over $\\mathbb F$, let $\\varrho _J$ denote the restriction (to $S$) of the congruence on ${\\mathbb F}[S]$ defined by the ideal $J$. A semigroup $S$ is called a permutable semigroup if $\\alpha \\circ \\beta =\\beta \\circ \\alpha$ is satisfied for all congruences $\\alpha$ and $\\beta$ of $S$. In this paper we show that if $S$ is a semilattice or a rectangular band then $\\varphi _{\\{S;{\\mathbb F}\\}}:\\ J\\mapsto \\varrho _J$ is a homomorphism of the semigroup $(Con ({\\mathbb F}[S]);\\circ )$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08671","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"}