#5485: issue with dimension of ideals in polynomial rings
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Reporter: AlexGhitza | Owner: malb
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: commutative algebra | Keywords:
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Comment(by john_perry):
Hi Alex,
What is EGA IV? If my university's library has it, I'd be glad to take a
look at it.
You wrote,
> I have just spent some quality time with EGA IV and found
> something that we can use: Corollary 5.5.4 (page 95 in
> volume 2 of EGA IV) says that if the ring A is noetherian,
> then the dimension of A[x_1,...,x_n] is equal to n + dim(A).
> ...
>
> So here's what we need to do for polynomial rings: check
> whether the base ring is noetherian; if not, raise a
> NotImplementedError. If yes, return the Krull dimension of
> the base ring plus the number of generators.
Hold on: {{{dimension()}}} is a method of an ideal, not of a ring. I can
see that this would work with (0), but will it work with other ideals?
i.e., can I assume that if R is Noetherian, then I should add the affine
dimension? (I'm not sure that ''affine dimension'' is the right term,
probably not, but I hope you get the idea.)
For example:
{{{
sage: R.<x,y> = ZZ[]
sage: I = R.ideal(x+y)
sage. I.dimension()
}}}
Should the answer be 1 (current) or 2 (my wholly uninformed guess, dim ZZ
+ affine dim of ideal) or something else?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5485#comment:4>
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