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Results tagged with ac.commutative-algebra
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user 117693
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
2
votes
0
answers
336
views
Lifting irreducibility of polynomials over an integral domain to the quotient field
Suppose $R$ is an integral domain with quotient field $K$ and $f \in R[x]$ is an irreducible polynomial.
Under what conditions on $R$ and $f$ can we conclude that $f$ is irreducible in $K[x]$?
It is …
- 804
12
votes
1
answer
641
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What kind of arithmetic information does the ring of integers in an infinite extension carry?
The fact that the ring of integers in a finite extension of $\Bbb Q$ is a Dedekind domain and purely algebraic properties of Dedekind domains are absolutely essential for algebraic number theory. So i …
- 804
10
votes
0
answers
184
views
Is every UFD a filtered colimit of Noetherian UFDs?
I'm wondering how one could prove or disprove that any non-Noetherian UFD is a filtered colimit of Noetherian UFDs. This would allow for some absolute Noetherian approximation to be applied for result …
- 804