We consider some results in a $Gamma$ - ring M with derivation which is related to Q, and the quotient $Gamma$ - ring of M.

Using fuzzy ideals, characterizations of Noetherian $Gamma$ -rings are given, and a condition for a $Gamma$ -ring to be Artinian is also given.

The converse of [7, Theorem 3.3] is provided. For an Artinian G-ring, a few results are investigated.