{"paper":{"title":"An Algorithm to Compute a Primary Decomposition of Modules in Polynomial Rings over the Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Afshan Sadiq, Gerhard Pfister, Nazeran Idrees","submitted_at":"2014-08-19T13:55:06Z","abstract_excerpt":"We present an algorithm to compute the primary decomposition of a submodule $\\mathcal{N}$ of the free module $\\Z[x_1, \\ldots, x_n]^m$. For this purpose we use algorithms for primary decomposition of ideals in the polynomial ring over the integers. The idea is to compute first the minimal associated primes of $\\mathcal{N}$, i.e. the minimal associated primes of the ideal $\\Ann(\\Z[x_1, \\ldots, x_n]^m /\\mathcal{N})$ in $\\Z[x_1,\\ldots,x_n]$ and then compute the primary components using pseudo-primary decomposition and extraction, following the ideas of Shimoyama-Yokoyama. The algorithms are implem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4343","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"}