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7.7.9.0. lpNoetherian
Procedure from library fpaprops.lib (see fpaprops_lib).
- Usage:
- lpNoetherian(G); G an ideal in a Letterplace ring
- Return:
- int
0 not Noetherian
1 left Noetherian
2 right Noetherian
3 Noetherian
4 weak Noetherian
- Purpose:
- Check whether the monomial algebra A/<LM(G)> is (left/right) noetherian
- Assume:
- - basering is a Letterplace ring
- G is a Groebner basis
- Theory:
- lpNoetherian works with the monomial algebra A/<LM(G)>.
If it gives an affirmative answer for one of the properties, then it
holds for both A/<LM(G)> and A/<G>. However, a negative answer applies
only to A/<LM(G)> and not necessarily to A/<G>.
- Note:
- Weak Noetherian means that two-sided ideals in A/<LM(G)> satisfy
the acc (ascending chain condition).
Example:
| LIB "fpaprops.lib";
ring r = 0,(x,y),dp;
def R = makeLetterplaceRing(5);
setring R;
ideal G = x(1)*x(2), y(1)*x(2); // K<x,y>/<xx,yx> is right noetherian
lpNoetherian(G);
==> 2
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