Abstract
ABSTRACT For any field F, we give an example of a prime finitely generated F-algebra of GK dimension 2 for which GK dimension is not finitely partitive. For each m ∈ {0, 1, 2, 3,…} ∪ {∞}, we give an example of a prime finitely generated F-algebra having GK dimension 2 which has classical Krull dimension m; the algebra of GK dimension 2 which has infinite classical Krull dimension has the additional property that it does not satisfy the ascending chain condition on prime ideals. This answers some questions of Bergman.
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