A gamma ring with minimum conditions

The aim of this note is to study the structure of a Γ-ring (not in the sense of Nobusawa) with minimum conditions. By ring theoretical techniques, we obtain various prooperties on the semi-prime Γ-ring and generalize Nobusawa\u27s result which corresponds to the Wedderburn-Artin Theorem in ring theory. Using these results, we have that a Γ-ring with minimum right and left condisions is homomorphic onto the Γo-ring Σ[?]=1Dn[?]. m(i), where Dn(t)(t), M(1) is the additive abelian group of the all rectangular matrices of type n(i)×(i) over some divison ring D(i), and Γo is a subdirect sum of the Γξ, 1≦i≦q which is a non-zero subgroup of Dm(t)(t), n(t) of type m(i)×(i) over D(i)