{"paper":{"title":"A Generalization of $\\Delta$U Rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Ahmad Moussavi, Mehrdad Esfandiar, Omid Hasanzadeh, Peter Danchev","submitted_at":"2026-05-21T16:43:08Z","abstract_excerpt":"In this paper, we introduce and study a new class of rings calling them {\\it weakly $\\Delta U$-rings}, hereafter abbreviated as {\\it $W\\Delta U$-rings} for short. A ring $R$ is said to be $W\\Delta U$ if every unit of $R$ can be expressed as $\\pm 1 + d$ for some $d \\in \\Delta(R)$, where $\\Delta(R)$ is the largest Jacobson radical of $R$ that is closed under multiplication by units.\n  Utilizing the known structure of $\\Delta(R)$, we investigate the relationships between $W\\Delta U$ rings and certain classical concepts such as $\\Delta U$-rings, $UJ$-rings, $WUJ$-rings, as well as clean and exchan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22700","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22700/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}