In this paper we discuss the von Neumann regular properties of the full matrix Γ-ring R. over a Γ-ring R

The follwing results are proved.1 If I is a ideal of the Γ-ring R then M(I_■)=(M(I))_■.2 Let R be a Γ-ring

then the full matrix Γ-ring R. is von Neumann regular if and only if R is von Neumann regular.3 Let R be a Γ-ring

H a set of the ideals of R

K a set of the ideals of R_■Then the mappiny φ: I→I_■ is a order-preserving monomorphism of H into K and the von Neumann regular ideals of R_■ are the sets corresponding to the von Neumann regular ideals of R.