Singular Manual: lpNoetherian

| #### 7.7.3.1 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*x, y*x; // K<x,y>/<xx,yx> is right noetherian
    lpNoetherian(G);
    ==> 3

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