How can we compute the localization of the ring $\mathbb{Z}/6\mathbb{Z}$ at the prime ideal $2\mathbb{Z}/\mathbb{6Z}$? (or how do we see that this localization is an integral domain)?
Localization at a prime ideal in $\mathbb{Z}/6\mathbb{Z}$
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abstract-algebra
ring-theory
commutative-algebra
localization
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0arent you inverting the zero divisor 3? – 2011-04-11
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3@yoyo: Yes, but $S$ containing a zerodivisor only implies that the canonical map $f:R\rightarrow S^{-1}R$ is not injective, as we would expect here. The map $f$ is only the zero map when $0\in S$. – 2011-04-11