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Let $g:B\\to C$ be a homomorphism of Noetherian $\\mathbb F_p$-algebras. If $g$ is faithfully flat reduced, and $C$ is $F$-finite, then $B$ is $F$-finite. This is a generalization of Seydi's result on excellent local rings of characteristic $p$."},"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":"1203.3640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-16T09:07:58Z","cross_cats_sorted":[],"title_canon_sha256":"f77ed74f8c2fc90356fc644f44e91dfb4b99689936e7fbee3e7102083da2138c","abstract_canon_sha256":"198af17cef742b01214279f03ed0b17f7dd94dffdcaf983074a7dd59460ae6d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:48.912184Z","signature_b64":"qMfupeeqW2/WjJTsVbLhlnMqr0R//X+UD7E8tE6IKCjrThnfrg+WMe01hiD2INXCfBhYRzvdvxjyI+P8Pi14Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92e20a0d778be95a33d6eeb32a3f743abd08f717a4c0d7d781a591a72b468981","last_reissued_at":"2026-05-18T03:59:48.911795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:48.911795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$F$-finiteness of homomorphisms and its descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mitsuyasu Hashimoto","submitted_at":"2012-03-16T09:07:58Z","abstract_excerpt":"Let $p$ be a prime number. We define the notion of $F$-finiteness of homomorphisms of $\\mathbb F_p$-algebras, and discuss some basic properties. In particular, we prove a sort of descent theorem on $F$-finiteness of homomorphisms of $\\mathbb F_p$-algebras. As a corollary, we prove the following. Let $g:B\\to C$ be a homomorphism of Noetherian $\\mathbb F_p$-algebras. If $g$ is faithfully flat reduced, and $C$ is $F$-finite, then $B$ is $F$-finite. 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