Let G be a group. Let R be a G-graded commutative ring with identity and let M be a graded R-module. The graded classical prime spectrum Cl.Spec g (M ) is defined to be the set of all graded classical prime submodule of M . In this paper we establish necessary and sufficient conditions for Cl.Spec g (M ) with the Zariski topology to be a Noetherian topological space.
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