{"paper":{"title":"The congruence $\\eta^{\\ast}$ on semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"M.H. Shahzamanian","submitted_at":"2014-10-08T17:33:28Z","abstract_excerpt":"In this paper we define a congruence $\\eta^{\\ast}$ on semigroups. For the finite semigroups $S$, $\\eta^{\\ast}$ is the smallest congruence relation such that $S/\\eta^{\\ast}$ is a nilpotent semigroup (in the sense of Malcev). In order to study the congruence relation $\\eta^{\\ast}$ on finite semigroups, we define a $\\textbf{CS}$-diagonal finite regular Rees matrix semigroup. We prove that, if $S$ is a $\\textbf{CS}$-diagonal finite regular Rees matrix semigroup then $S/\\eta^{\\ast}$ is inverse. Also, if $S$ is a completely regular finite semigroup, then $S/\\eta^{\\ast}$ is a Clifford semigroup.\n  We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2194","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"}