Timeline for Rings of algebraic integers as quotients of polynomial rings

8 events

when toggle format	what		by	license	comment
S Oct 24, 2014 at 16:39	history	suggested	PedroJVM		Just adding tag to promote diffusion. This problem bridges Comp. Alg. Number Theory to Comp. Comm. Algebra.
Oct 24, 2014 at 16:21	review	Suggested edits
S Oct 24, 2014 at 16:39
Oct 9, 2014 at 23:01	comment	added	tj_		@Albertas: Yes, it's indeed imprecise. The correct statement is that $p$ is generated by polynomials of content $1$.
Oct 9, 2014 at 13:43	comment	added	Albertas		2 tj_ : the remark about content seems imprecise ($2f$ must be also be in $\mathfrak{p}$, since $\mathfrak{p}$ is an ideal).
Oct 9, 2014 at 13:34	comment	added	Albertas		Thank you; I was not aware of the result of P.A.B. Pleasants that mostly clarifies ii). For i), many quotients of one-variable polynomial ring would fail to be rings of integers e.g., for reasons other that already mentioned by tj_; since question i) is not well-defined, I am glad for any remarks that makes the setting clearer.
Oct 9, 2014 at 11:55	comment	added	tj_		For (i): Obvious restrictions for $p$ are: $\text{codim}(p)=1$; $p \cap \mathbb{Z}=0$; there is some $f \in p$ such that $f(0)\neq 0$; the content of each $f \in p$ is $1$.
Oct 9, 2014 at 10:36	comment	added	KConrad		For (ii), see mathoverflow.net/questions/21267/…, including the comments.
Oct 9, 2014 at 10:30	history	asked	Albertas	CC BY-SA 3.0