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Results tagged with ideals
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user 88133
4
votes
Accepted
Condition for a monomial to belong to a particular ideal
Such a value $d$ does not necessarily exist. For $J=(xy,xz)$ we have $(xyz)^{d-1} \notin J^d$ for any $d$. It’s even worse (but maybe a little degenerate) if $J$ is principal.
A necessary and suffici …
- 6,237
1
vote
Accepted
Is this algorithm for primary decomposition correct?
(Just making an answer out of the above comment, with a small modification.) I think this will have problems if the ideal's generators don't factor at all. For example, for an ideal like
$$
(y^2 - x …
- 6,237
5
votes
Accepted
Ideals: If $\langle f_1,f_2 \rangle = \langle g_1,g_2 \rangle$, then $\langle f_1-\lambda,f_...
The ideals $\langle x, y(1-xy) \rangle$ and $\langle x, y \rangle$ are equal, and maximal; but
$$ \langle x-\lambda, y(1-xy)\rangle \neq \langle x-\delta, y-\epsilon \rangle$$
for any $\lambda,\delta,\ …
- 6,237