On the Unity in Γ-rings

The unity for multiplication in Γ-rings is more complicated and changeful than that in associative rings. First it is classified to be unity or a-unity (strong unity). Secondly it possesses different properties with that in associative rings. These properties are expounded in this paper. The relation between the unities in Γ-ring M and in its matrix ring M_m,n is studied. This relation has feature of Γ-rings too. Lastly the characteristic chM of Γ-ring M is introduc-ed, Some properties of chM are proved for M with unities.