The only examples of commutative rings of finite global dimension I know are either:
- Dedekind domains (and fields as a degenerate special case)
- Regular local rings
- Rings constructed from the previous examples by taking direct sums, or forming the rings of polynomials over a ring of finite global dimension.
Are there other examples? In particular, are there other examples that are finite-dimensional over a field $k$?
(Examples of rings of finite global dimension are easier to come by in the noncommutative case, but I'm specifically curious about the commutative case.)