Affineness on Noetherian graded rings, algebras and Hopf algebras
Abstract
In this note, we show that every Noetherian graded ring with an affine degree zero part is affine. As a result, a Noetherian graded Hopf algebra whose degree zero component is a commutative or a cocommutative Hopf subalgebra is affine. Moreover, we show that the braided Hopf algebra of a Noetherian graded Hopf algebra is affine.
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