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June 12th, 2011, 03:17 AM   #1
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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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