{"paper":{"title":"On Modulo AG-groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Amanullah, Imtiaz Ahmad, Muhammad Rashad, Muhammad Shah","submitted_at":"2014-03-11T13:11:17Z","abstract_excerpt":"A groupoid G is called an AG-groupoid if it satisfies the left invertive law: (ab)c = (cb)a. An AG-group G, is an AG-groupoid with left identity e \\in G (that is, ea = a for all a \\in G) and for all a \\in G there exists a' \\in G such that a.a' = a'.a = e. In this article we introduce the concept of AG-groupoids (mod n) and AG-group (mod n) using Vasantha's constructions [1]. This enables us to prove that AG-groupoids (mod n) and AG-groups (mod n) exist for every integer n \\geq 3. We also give some nice characterizations of some classes of AG-groupoids in terms of AG-groupoids (mod n)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2564","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"}