{"paper":{"title":"On the Zariski topology of $\\Omega$-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ruvim Lipyanski","submitted_at":"2017-12-11T14:56:21Z","abstract_excerpt":"A number of geometric properties of $\\Omega$-groups from a given variety of $\\Omega$-groups can be characterized using the notions of domain and equational domain. An $\\Omega$-group $H$ of a variety $\\Theta$ is an equational domain in $\\Theta$ if the union of algebraic varieties over $H$ is an algebraic variety. We give necessary and sufficient conditions for an $\\Omega$-group $H$ in $\\Theta$ to be an equational domain in this variety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03801","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"}