if R is a ring, why is there an isomorphism between R/R and {0}?

I don't understand how is it even possible because R/R = R.

Thanks.

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- Feb 3rd 2011, 09:07 AMGinsburgIsomorphism between R/R and {0}
if R is a ring, why is there an isomorphism between R/R and {0}?

I don't understand how is it even possible because R/R = R.

Thanks. - Feb 3rd 2011, 09:29 AMFernandoRevilla
$\displaystyle [x],[y]\in R/R$

are equal iff

$\displaystyle x-y\in R$

This happen for all $\displaystyle x,y\in R$ so, $\displaystyle R/R$ has only one element:

$\displaystyle R/R=\{[0]\}$

Fernando Revilla