{"paper":{"title":"Elementary matrix factorizations over B\\'ezout domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.AC","authors_text":"Calin Iuliu Lazaroiu, Dmitry Doryn, Mehdi Tavakol","submitted_at":"2018-01-08T10:29:09Z","abstract_excerpt":"We study the homotopy category $\\mathrm{hef}(R,W)$ (and its $\\mathbb{Z}_2$-graded version $\\mathrm{HEF}(R,W)$) of elementary factorizations, where $R$ is a B\\'ezout domain which has prime elements and $W=W_0 W_c$, where $W_0\\in R^\\times$ is a square-free element of $R$ and $W_c\\in R^\\times$ is a finite product of primes with order at least two. In this situation, we give criteria for detecting isomorphisms in $\\mathrm{hef}(R,W)$ and $\\mathrm{HEF}(R,W)$ and formulas for the number of isomorphism classes of objects. We also study the full subcategory $\\mathbf{hef}(R,W)$ of the homotopy category "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02369","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"}