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Let R be a ring graded by a finite group G with the identity component Re and let M be a left R-module. It is proved that GdimR M = GdimRe M, KdimR M = KdimRe M and NdimR M = NdimRe M, where Gdim, Kdim and Ndim denote, respectively, Gabriel, Krull and dual Krull dimensions. The proofs are based on the use of lattice theory, a method which also gives alternative proofs of known results about normalizing extensions.

Gabriel and Krull Dimensions of Modules Over Rings Graded by Finite Groups