{"paper":{"title":"Stable equivalence of Morita type and Frobenius extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"M. Beattie, S. Caenepeel, S. Raianu","submitted_at":"2012-02-11T13:05:23Z","abstract_excerpt":"A.S. Dugas and R. Mart\\'{i}nez-Villa proved in \\cite[Corollary 5.1]{dm} that if there exists a stable equivalence of Morita type between the $k$-algebras $\\Lambda$ and $\\Gamma$, then it is possible to replace $\\Lambda$ by a Morita equivalent $k$-algebra $\\Delta$ such that $\\Gamma$ is a subring of $\\Delta$ and the induction and restriction functors induce inverse stable equivalences. In this note we give an affirmative answer to a question of Alex Dugas about the existence of a $\\Gamma$-coring structure on $\\Delta$. We do this by showing that $\\Delta$ is a Frobenius extension of $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2441","kind":"arxiv","version":1},"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"}