{"paper":{"title":"Generators and presentations for direct and wreath products of monoid acts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Craig Miller","submitted_at":"2018-04-06T11:24:57Z","abstract_excerpt":"We investigate the preservation of the properties of being finitely generated and finitely presented under both direct and wreath products of monoid acts. A monoid $M$ is said to preserve property $\\mathcal{P}$ in direct products if, for any two $M$-acts $A$ and $B$, the direct product $A\\times B$ has property $\\mathcal{P}$ if and only if both $A$ and $B$ have property $\\mathcal{P}$. It is proved that the monoids $M$ that preserve finite generation (resp. finitely presentability) in direct products are precisely those for which the diagonal $M$-act $M\\times M$ is finitely generated (resp. fini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03010","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"}