{"paper":{"title":"Davenport constant of the multiplicative semigroup of the ring $\\mathbb{Z}_{n_1}\\oplus\\cdots\\oplus \\mathbb{Z}_{n_r}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang, Weidong Gao","submitted_at":"2016-03-19T01:57:02Z","abstract_excerpt":"Given a finite commutative semigroup $\\mathcal{S}$ (written additively), denoted by ${\\rm D}(\\mathcal{S})$ the Davenport constant of $\\mathcal{S}$, namely the least positive integer $\\ell$ such that for any $\\ell$ elements $s_1,\\ldots,s_{\\ell}\\in \\mathcal{S}$ there exists a set $I\\subsetneq [1,\\ell]$ for which $\\sum_{i\\in I} s_i=\\sum_{i=1}^{\\ell} s_i$.\n  Then, for any integers $r\\geq 1, n_1,\\ldots,n_r>1$, let $R=\\mathbb{Z}_{n_1}\\oplus\\cdots\\oplus \\mathbb{Z}_{n_r}$ be the direct sum of these $r$ residue class rings $\\mathbb{Z}_{n_1}, \\ldots,\\mathbb{Z}_{n_r}$. Moreover, let $\\mathcal{S}_R$ be th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06030","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"}