Integral domain

Groups, Rings, Domains, Modules, etc, Galois theory
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Papapetros Vaggelis
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Joined: Mon Nov 09, 2015 1:52 pm

Integral domain

#1

Post by Papapetros Vaggelis »

Let \(\displaystyle{\left(R,+,\cdot\right)}\) be a commutative ring with unity. If the local ring

\(\displaystyle{R_{p}}\) (localization of R to P) is an integral domain for every \(\displaystyle{P\in\rm{Spec}(R)}\),

then decide if the ring \(\displaystyle{\left(R,+,\cdot\right)}\) is an integral domain or not.
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