When does $(a,b)=(gcd(a,b))$ hold?
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I had a look here to understand why $K[X,Y]$ is not a PID. So one of the conclusions was that $(x,y) neq (1) = gcd(x,y)$ , but I thought that $(a,b)=gcd(a,b)$ was always true so obviously I was wrong. But when exactly does this relation hold then, if $ a,b in R$ and $R$ is a ring?
ring-theory ideals greatest-common-divisor principal-ideal-domains
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edited Nov 19 at 13:22
amWhy
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asked Nov 19 at 11:45
roi_saumon