Andrei V. Kelarev
Abstract
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For any ring R graded by a finite group, we give a bound on the classical Krull dimension of R in terms of the dimension of the initial component Re. It follows that if Re has finite classical Krull dimension, then the same is true of the whole ring R, too.
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For any ring R graded by a finite group, we give a bound on the classical Krull dimension of R in terms of the dimension of the initial component Re. It follows that if Re has finite classical Krull dimension, then the same is true of the whole ring R, too.
Key concepts: Krull dimension, Mathematics, Global dimension, Dimension theory (algebra), Dimension (graph theory), Regular local ring, Ring (chemistry), Pure mathematics