In the current paper, we investigate the properties of commutative \(\Gamma \) -rings with a unity element \(1_{\gamma _0}\) . Specifically, we extend Cohen’s theorem, which states that “a commutative ring with unity R is Noetherian if and only if each of its prime ideals is finitely generated”, to this broader class of algebraic structures. Our approach involves characterizing Noetherian \(\Gamma \) -rings in terms of maximality and finitely generated \(\Gamma \) -ideals. We prove a key corollary that describes the \(\Gamma \) -ideal generated by a nonempty subset of a commutative \(\Gamma \) -ring. Finally, we provide the proof of the main result, demonstrating that under certain conditions, the theorem holds for commutative \(\Gamma \) -rings. These results provide new insights into the structure and classification of \(\Gamma \) -rings, with potential implications for further research in this area.