On Quasi-Cancellativity of AG-Groupoids
Muhammad Shah, Imtiaz Ahmad, Asif Ali · 2012
Quasi-cancellativity is the generalization of cancellativity. We introduce the notion of quasi-cancellativity of semigroup into AG-groupoids. We prove that every AG-band is quasi-cancellative. We also prove the famous Burmistrovich’s Theorem for AG-groupoids that states “An AG ∗∗ -groupoid S is a quasi-cancellative if and only if S is a semilattice of cancellative AG ∗∗ -groupoids”.