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Sample solutions of selected problems from Sets 10 and 11 Chris Peterson and Hirotachi Abo
 

Summary: Sample solutions of selected problems from Sets 10 and 11
Chris Peterson and Hirotachi Abo
All the computations will be done over the rationals Q. Let k =QQ.
i1 : KK=QQ;
Problem 2 (Set 10). Let I = (x3
y - x2
, x2
- xy) be an ideal in k[x, y]. We
compute the ideal quotient I : x2
by taking the following steps:
(1) Compute the intersection of the ideal I and (x2
);
(2) Let (h1, . . . , ht) be the intersection of these two ideal obtained in (1).
Compute (h1/x2
, . . . , ht/x2
).
The result in (2) equals the ideal quotient I : x2
.
(1) Let L be the ideal in k[t, x, y] defined by tI + (1 - t)(x2
). Recall that

  

Source: Abo, Hirotachi - Department of Mathematics, University of Idaho

 

Collections: Mathematics