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Results tagged with power-series
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user 4790
24
votes
Accepted
What are the prime ideals of k[[x,y]]?
The ring $k[[x,y]]$ is a local UFD of dimension 2; so its prime ideals are the zero ideal, the maximal ideal, and all the ideals generated by an irreducible element. They are all closed (all ideals in …
- 27k
15
votes
Accepted
flatness of power series rings
As a module, $A[[X]]$ is the product of a countable family of copies of $A$. It is known that the product of flat $A$-modules is flat if and only if the ring $A$ is coherent, that is, every finitely g …
- 27k