2014/02/21 by Muhammad Rashad, Rashad, Muhammad, Imtiaz Ahmad +5
Decision Sciences · Computer Science · #Fuzzy and Soft Set Theory #Constraint Satisfaction and Optimization
paper · pdf · doi:10.48550/arxiv.1402.5296
An AG-groupoid is an algebraic structure that satisfies the left invertive law: (ab)c =(cb)a. We prove that the class of left transitive AG-groupoids (AG-groupoids satisfying the identity, ab.ac = bc) coincides with the class of T2-AG-groupoids. We also develop a simple procedure to test whether an arbitrary groupoid is left transitive AG-groupoid or not. Further we prove that, (i). Every left transitive AG-groupoid is transitively commutative AG-groupoid (ii) For left transitive AG-groupoid the properties of flexibility, right alternativity, AG*, right nuclear square, middle nuclear square and commutative semigroup are equivalent.