is the localisation of the ring $$A:=\mathbb{Z}_p[T]/(pT^2+T+1)$$ at the prime ideal (p) isomorphic to $\mathbb{Z}_p$?
If not, how to understand this ring very explicitly?
about the local ring of $\mathbb{Z}_p[T]/(pT^2+T+1)$ at the prime p
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