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Given a left noetherian k-algebra A graded by a group G, an injective objectI in the category of G-graded A-modules and a morphism from G to another groupG', we provide bounds for the injective dimension of I as a G'-graded A-module.For this, we use three change of grading functors. Most of the constructionsconcerning these functors work in the context of H-comodule algebras, where His a Hopf algebra, so we develop them in this general context.

Behaviour of injective dimension with respect to regradings