{"paper":{"title":"On the Nullstellens\\\"atze for Stein spaces and $C$-analytic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fabrizio Broglia, Francesca Acquistapace, Jose F. Fernando","submitted_at":"2012-07-02T14:04:42Z","abstract_excerpt":"In this work we prove the real Nullstellensatz for the ring ${\\mathcal O}(X)$ of analytic functions on a $C$-analytic set $X\\subset{\\mathbb R}^n$ in terms of the saturation of \\L ojasiewicz's radical in ${\\mathcal O}(X)$: The ideal ${\\mathcal I}({\\mathcal Z}({\\mathfrak a}))$ of the zero-set ${\\mathcal Z}({\\mathfrak a})$ of an ideal ${\\mathfrak a}$ of ${\\mathcal O}(X)$ coincides with the saturation $\\widetilde{\\sqrt[\\text{\\L}]{{\\mathfrak a}}}$ of \\L ojasiewicz's radical $\\sqrt[\\text{\\L}]{{\\mathfrak a}}$. If ${\\mathcal Z}({\\mathfrak a})$ has `good properties' concerning Hilbert's 17th Problem, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0391","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"}