{"paper":{"title":"A Classification of Regressive Transformation Semigroups on Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Patanee Udomkavanich, Phichet Jitjankarn","submitted_at":"2011-05-25T02:28:39Z","abstract_excerpt":"For each subchain $X'$ of a chain $X$, let $T_{RE}(X, X')$ denote the semigroup under composition of all full regressive transformations, $\\alpha:X\\rightarrow X'$ satisfying $x\\alpha\\leq x$ for all $x\\in X$. Necessary and sufficient conditions for $T_{RE}(X,X')$ and $T_{RE}(Y,Y')$ to be isomorphic are given. This isomorphism theorem is applied to classify the semigroup of regressive transformations $T_{RE}(X,X')$ where $X$ are familiar subchains of $\\R$, the chain of real numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4922","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"}