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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.03010","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-06T11:24:57Z","cross_cats_sorted":[],"title_canon_sha256":"45be9be6b9659a9d432c9d190e1cd963ae882e9f3f36de1787842a37784dd043","abstract_canon_sha256":"40e08f826ec2e00322337993430084447d639a95d293ae6fc0f38ff608b7f864"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:41.735389Z","signature_b64":"tO/yaCd352NzoFVWZVgsXhiJAEdmnmKZaIKVoNI89CsSeJD3NLi1YNaQoRc31TluKZyAWcMbwTyzdaCBscfFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6359806772dd1fadd78e7a856db249c297d76fe9cad644134b507729407eb15e","last_reissued_at":"2026-05-17T23:58:41.734719Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:41.734719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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