{"paper":{"title":"Topological properties of semigroup primes of a commutative ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Carmelo A. Finocchiaro, Dario Spirito, Marco Fontana","submitted_at":"2017-03-29T17:35:28Z","abstract_excerpt":"A semigroup prime of a commutative ring $R$ is a prime ideal of the semigroup $(R,\\cdot)$. One of the purposes of this paper is to study, from a topological point of view, the space $\\scal(R)$ of prime semigroups of $R$. We show that, under a natural topology introduced by B. Olberding in 2010, $\\scal(R)$ is a spectral space (after Hochster), spectral extension of $\\Spec(R)$, and that the assignment $R\\mapsto\\scal(R)$ induces a contravariant functor. We then relate -- in the case $R$ is an integral domain -- the topology on $\\scal(R)$ with the Zariski topology on the set of overrings of $R$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10153","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"}