{"paper":{"title":"About multiplicities and applications to Bezout numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"M. Azeem Khadam, Peter Schenzel","submitted_at":"2017-12-29T08:32:22Z","abstract_excerpt":"Let $(A,\\mathfrak{m},\\Bbbk)$ denote a local Noetherian ring and $\\mathfrak{q}$ an ideal such that $\\ell_A(M/\\mathfrak{q}M) < \\infty$ for a finitely generated $A$-module $M$. Let $\\au = a_1,\\ldots,a_d$ denote a system of parameters of $M$ such that $a_i \\in \\mathfrak{q}^{c_i} \\setminus \\mathfrak{q}^{c_i+1}$ for $i=1,\\ldots,d$. It follows that $ \\chi := e_0(\\au;M) - c \\cdot e_0(\\mathfrak{q};M) \\geq 0$, where $c = c_1\\cdot \\ldots \\cdot c_d$. The main results of the report are a discussion when $\\chi = 0$ resp. to describe the value of $\\chi$ in some particular cases. Applications concern results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10144","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"}