{"paper":{"title":"On the complete intersection conjecture of Murthy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Satya Mandal","submitted_at":"2015-09-28T23:09:32Z","abstract_excerpt":"Suppose $A=k[X_1, X_2, \\ldots, X_n]$ is a polynomial ring over a field $k$ and $I$ is an ideal in $A$. Then M. P. Murthy conjectured that $\\mu(I)=\\mu(I/I^2)$, where $\\mu$ denotes the minimal number of generators. Recently, Fasel \\cite{F} settled this conjecture, affirmatively, when $k$ is an infinite perfect field, with $1/2\\in k$ {\\rm (always)}. We are able to do the same, when $k$ is an infinite field. In fact, we prove similar results for ideals $I$ in a polynomial ring $A=R[X]$, that contains a monic polynomial and $R$ is essentially finite type smooth algebra over an infinite field $k$, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08534","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"}