{"paper":{"title":"On additivity of local entropy under flat extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mahdi Majidi-Zolbanin","submitted_at":"2014-04-06T02:35:25Z","abstract_excerpt":"Let $f\\colon(R,\\mathfrak{m})\\rightarrow S$ be a local homomorphism of Noetherian local rings. Consider two endomorphisms \\textit{of finite length} (i.e., with zero-dimensional closed fibers) $\\varphi\\colon R\\rightarrow R$ and $\\psi\\colon S\\rightarrow S$, satisfying $\\psi\\circ f=f\\circ\\varphi$. Then $\\psi$ induces a finite length endomorphism $\\overline{\\psi}\\colon S/f(\\mathfrak{m})S\\rightarrow S/f(\\mathfrak{m})S$. When $f$ is flat, under the assumption that $S$ is Cohen-Macaulay we prove an additivity formula: $h_{\\mathrm{loc}}(\\psi)=h_{\\mathrm{loc}}(\\varphi)+h_{\\mathrm{loc}}(\\overline{\\psi})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1541","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"}