{"paper":{"title":"Hom-associative magmas with applications to Hom-associative magma algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Patrik Lundstr\\\"om","submitted_at":"2023-08-04T14:16:37Z","abstract_excerpt":"Let $X$ be a magma, that is a set equipped with a binary operation, and consider a function $\\alpha : X \\to X$. We that $X$ is Hom-associative if for all $x,y,z \\in X$, the equality $\\alpha(x)(yz) = (xy) \\alpha(z)$ holds. For every isomorphism class of magmas of order two, we determine all functions $\\alpha$ making $X$ Hom-associative. Furthermore, we find all such $\\alpha$ that are endomorphisms of $X$. We also consider versions of these results where the binary operation on $X$ as well as the function $\\alpha$ may be only partially defined. We use our findings to construct examples of Hom-as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.02341","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.02341/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}