{"paper":{"title":"On the Erd\\H{o}s-Burgess constant of the multiplicative semigroup of a factor ring of $\\mathbb{F}_q[x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Haoli Wang, Jun Hao, Lizhen Zhang","submitted_at":"2018-05-06T08:03:37Z","abstract_excerpt":"Let $\\mathcal{S}$ be a commutative semigroup endowed with a binary associative operation $+$. An element $e$ of $\\mathcal{S}$ is said to be idempotent if $e+e=e$. The {\\sl Erd\\H{o}s-Burgess constant} of $\\mathcal{S}$ is defined as the smallest $\\ell\\in \\mathbb{N}\\cup \\{\\infty\\}$ such that any sequence $T$ of terms from $S$ and of length $\\ell$ contains a nonempty subsequence the sum of whose terms is idempotent. Let $q$ be a prime power, and let $\\F_q[x]$ be the polynomial ring over the finite field $\\F_q$. Let $R=\\F_q[x]\\diagup K$ be a quotient ring of $\\F_q[x]$ modulo any ideal $K$. We gave "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02166","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"}