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Results tagged with reference-request
Search options answers only
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user 86006
This tag is used if a reference is needed in a paper or textbook on a specific result.
3
votes
Level of a commutative ring and its quotient field
Let me assume that $2$ is invertible in $A$.
Regarding question 2, for a regular local ring $A$ with fraction field $F$ and $s(F)=2^k$, the equality $s(A)=s(F)$ follows from the Gorthendieck--Serre co …
- 2,928
3
votes
Accepted
Splitting of short exact sequence in the category of finitely generated modules over a commu...
Reiner's "Maximal Orders", Theorem 3.20, for instance.
- 2,928
6
votes
Literature Request: The derived category is Krull-Schmidt
I do not know a source showing this directly, but you can get it by combining two sources.
Let us write $k$ for the base field. By a theorem of Balmer and Schlichting (Thm. 2.8 here), the category $K^ …
- 2,928
3
votes
Accepted
Does Noetherianity imply division theorem?
This is a consequence of the noetherianity of $\mathcal{O}_n$, in some way.
Let me write $A_n$ for the ring of real formal formal series around the origin, i.e., $A_n=\mathbb{R}[[t_1,\dotsc,t_n]]$. Le …
- 2,928