Examples in Finite Gel'fand–Kirillov Dimension. II

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.

Keywords:

• Finitely partitive
• GK dimension
• Krull dimension

Mathematics Subject Classification:

• Primary 16P90
• Secondary 16P70

ACKNOWLEDGMENT

I thank Lance W. Small and the referee for many helpful comments and suggestions.

Notes

^#Communicated by J. Bell.