2014/03/11 by Muhammad Rashad, Amanullah, Rashad, Muhammad +4
Decision Sciences · Mathematics · #20L05 #20N05 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1403.2564
openalex publication_date 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ∈ G (that is, ea = a for all a ∈ G) and for all a ∈ G there exists a' ∈ 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 ≥ 3. We also give some nice characterizations of some classes of AG-groupoids in terms of AG-groupoids (mod n).