#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 AlexGhitza):
Hi John,
I've learned the hard way not to expect dimension to behave coherently
when the base ring is not a field. This being said, 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).
There are examples due to Nagata of non-noetherian rings A such that
dim(A)=1 but dim(A[x])=3.
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.
If you want to go ahead and do this, that's great. If not I can probably
get around to it sometime before this weekend.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5485#comment:3>
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