{"paper":{"title":"Factorizations in bounded hereditary Noetherian prime rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Daniel Smertnig","submitted_at":"2016-05-30T15:22:59Z","abstract_excerpt":"If $H$ is a monoid and $a=u_1 \\cdots u_k \\in H$ with atoms (irreducible elements) $u_1, \\ldots, u_k$, then $k$ is a length of $a$, the set of lengths of $a$ is denoted by $\\mathsf L(a)$, and $\\mathcal L(H)=\\{\\,\\mathsf L (a) \\mid a \\in H \\,\\}$ is the system of sets of lengths of $H$. Let $R$ be a hereditary Noetherian prime (HNP) ring. Then every element of the monoid of non-zero-divisors $R^\\bullet$ can be written as a product of atoms. We show that, if $R$ is bounded and every stably free right $R$-ideal is free, then there exists a transfer homomorphism from $R^{\\bullet}$ to the monoid $B$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09274","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"}