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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Re: Bezout's lemma?''
by drini on 2002-05-27 23:33:18 |
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| YEs Bezout lemma is a well known result of algebraic geometry that roughly relates the degree of 2 polynomials with the number of points in which they can intersect. So when I saw this entry I was shocked. Is there any possibility that you might have got a wrong name? I've never heard of this being called Bezout's lemma.
And for Euclid's algorithm, this isn't the Euclid's algorithm either. The Euclid's Algorithm (well it's extended version) is the PROCEDURE used to find this expression (and gcd).
And, you guys should be aware that both Euclid's algorithm and this result (I won't call it Bezout)
are just particular cases of Euclid's algorithm on a special kind of rings: Euclidean domains.
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f |
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