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We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions. Further, let $A$ and $B$ be finite-dimensional algebras over a field $k$, and let $\\dm(_AX)$ stand for the dominant dimension of an $A$-module $X$. If $_BM_A$ is a Frobenius bimodule, then $\\dm(A)\\le \\dm(_BM)$ and $\\dm(B)\\le \\dm(_A\\Hom_B(M, B))$."},"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":"1903.07921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-19T10:21:34Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"c7718c469b91f1d8411047a4c97be3bd5374bd82d365228c8ff1e2c2348fc598","abstract_canon_sha256":"7cd5a09d44ba5184d01f3806fe18f59255638d88f7254c541da09a173521c5e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:53.471477Z","signature_b64":"ZjRzyu4E3E3pdut7uyyqbBf+ONpXBv3DBGJDirEIdd8Zva1GJ5OtwFvg1zMGVQgJJKkpLXQHqXh6B+3pgCguAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9bcddcb3d871ac820bad500423aca38b350d839d1619bd8227114bdbd0f73b0","last_reissued_at":"2026-05-17T23:50:53.470691Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:53.470691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frobenius bimodules and flat-dominant dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Changchang Xi","submitted_at":"2019-03-19T10:21:34Z","abstract_excerpt":"We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules. This is motivated by the Nakayama conjecture and an approach of Martinez-Villa to the Auslander-Reiten conjecture on stable equivalences. We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions. Further, let $A$ and $B$ be finite-dimensional algebras over a field $k$, and let $\\dm(_AX)$ stand for the dominant dimension of an $A$-module $X$. 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