The paper introduces Hilbert-Serre rings and proves dim_gr(R) ≤ dim(R) ≤ GKdim_k(R) ≤ d(R) for them, with equality holding for monomial algebras.
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On Krull's Dimension Theorem for Certain Graded Rings and Its Applications
The paper introduces Hilbert-Serre rings and proves dim_gr(R) ≤ dim(R) ≤ GKdim_k(R) ≤ d(R) for them, with equality holding for monomial algebras.