{"paper":{"title":"On Special Semigroups Derived From an Arbitrary Semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Attila Nagy","submitted_at":"2015-10-18T18:21:03Z","abstract_excerpt":"Let $S$ be a semigroup, $\\Lambda$ a non-empty set and $P$ a mapping of $\\Lambda$ into $S$. The set $S\\times \\Lambda$ together with the operation $\\circ _P$ defined by $(s, \\lambda)\\circ _P(t, \\mu )=(sP(\\lambda)t, \\mu )$ form a semigroup which is denoted by $(S, \\Lambda , \\circ _P)$. Using this construction, we prove a common connection between the semigroups $S$, $S/\\theta$ and $S/\\theta ^*=(S/\\theta)/(\\theta ^*/\\theta)$, where $\\theta$ and $\\theta ^*/\\theta$ are the kernels of the right regular representations of $S$ and $S/\\theta$, respectively. We also prove an embedding theorem for the sem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05291","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"}