{"paper":{"title":"On Regular Sequences in the Form Module with Applications to Local B\\'ezout Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"M. Azeem Khadam","submitted_at":"2017-05-11T06:08:37Z","abstract_excerpt":"Let $\\mathfrak{q}$ denote an ideal in a Noetherian local ring $(A,\\mathfrak{m})$. Let $\\underline{a}=a_1,\\ldots,a_d \\subset \\mathfrak{q}$ denote a system of parameters in a finitely generated $A$-module $M$. This note investigate an improvement of the inequality $c_1\\cdot \\ldots \\cdot c_d \\cdot e_0(\\mathfrak{q};M) \\leq \\ell_A(M/\\underline{a}\\,M)$, where $c_i$ denote the initial degrees of $a_i$ in the form ring $G_A(\\mathfrak{q})$. To this end, there is an investigation of regular sequences in the form module $G_M(\\mathfrak{q})$ by homology of a factor complex of the Koszul complex. In a parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04024","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"}