An \(A\)-hypergroup \(H\) is a canonical hypergroup such that for all \(x\in H\) the set \(x-x\) is a subhypergroup of \(H\). The core \(\omega_ H\) of a hypergroup \(H\) is the smallest sub-hypergroup \(h\) of \(H\) such that the quotient \(H/h\) is a group. In the paper it is proved that in some \(A\)- hypergroups the core is equal to a hyperaddition of type zero while in others it is not. The extension of canonical hypergroups and \(A\)- hypergroups is also studied.