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June 12th, 2011, 02:17 AM  #1 
Newbie Joined: May 2011 From: Thisted, Denmark Posts: 13 Thanks: 0  Reduced Gröbner basis
Hi! This is exercise 5.19 in the book "Concrete Abstract Algebra" by Lauritzen. 19. Compute the reduced Gröbner basis of (X² + Y, X + Y) using the lexicographic ordering X greater than or equal to Y. If (X² + Y, X + Y) is a Gröbner basis, then the reduced basis should be ( X + Y), since X divides X², Definition 5.8.2 in the book. But isn't the exercise missing something ? Shouldn't you calculate if (X² + Y, X + Y) is a Gröbner basis for some ideal ? Martin. 

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basis, gröbner, reduced 
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