#15745: The unit ideal is not prime or primary
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Reporter: cremona | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.1
Component: algebra | Keywords: unit prime primary ideal
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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On sage-support on 2014-01-27, Jack <[email protected]> reported:
{{{
I'm a bit confused about Sage's answer if Ideal(1) is prime.
R.<x,y>= QQ[]
I = Ideal(R(1))
I.is_prime()
Sage (5.11, not only) says yes,
conflicting to the definition, http://en.wikipedia.org/wiki/Prime_ideal
Has somebody an expanation of this behaviour?
}}}
and in the following discussion it was agreed that this is incorrect, as
is {{{I.is_primary()}} (gives True not False) and
{{{I.primary_decomposition()}}} (gives a nonempty list) and
{{{I.is_maximal())}} (raises an error instead of returning False).
This originates with Singular, but could easily be fixed in Sage.
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Ticket URL: <http://trac.sagemath.org/ticket/15745>
Sage <http://www.sagemath.org>
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