{"paper":{"title":"Additively irreducible sequences in commutative semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang","submitted_at":"2015-04-26T13:16:53Z","abstract_excerpt":"Let $\\mathcal{S}$ be a commutative semigroup, and let $T$ be a sequence of terms from the semigroup $\\mathcal{S}$. We call $T$ an (additively) {\\sl irreducible} sequence provided that no sum of its some terms vanishes. Given any element $a$ of $\\mathcal{S}$, let ${\\rm D}_a(\\mathcal{S})$ be the largest length of the irreducible sequence such that the sum of all terms from the sequence is equal to $a$. In case that any ascending chain of principal ideals starting from the ideal $(a)$ terminates in $\\mathcal{S}$, we found the sufficient and necessary conditions of ${\\rm D}_a(\\mathcal{S})$ being f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06818","kind":"arxiv","version":3},"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"}