I am wondering if the following rings are catenary:

- If $k$ is a field, is the ring of formal power series $k[[X_1,\dots,X_n]]$ catenary?
- Is the ring of complex power series with a non-zero radius of convergence $\Bbb C\{X_1,\dots,X_n\}$ (
*id est*the ring of germs of holomorphic functions at zero) a catenary ring?

regularring. In his answer, Leo Alonso observes that these rings are in fact regular. So basically, the question asks "are these rings nice in a weak sense", and the answer is "yes, and don't worry -- they're actually nice in the strongest possible sense"! $\endgroup$