query: Prove $\{a(c):a(x) \in F[x]\}$ is an integral domain isomorphic to $F[x]$
positive_passages.docid: 150329
positive_passages.text: Simple extension fields
negative_passages.docid: 7011
negative_passages.text: Integral domain with fraction field equal to $\mathbb{R}$
negative_passages.docid: 8317
negative_passages.text: Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
negative_passages.docid: 80961
negative_passages.text: Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
negative_passages.docid: 141156
negative_passages.text: The domain of $\ln(x)^{\ln(x)}$
negative_passages.docid: 101637
negative_passages.text: Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
negative_passages.docid: 94819
negative_passages.text: Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
negative_passages.docid: 45720
negative_passages.text: Prove that $∂A$ is closed given $∂A = \text{Cl}(A) − \text{Int}(A)$
negative_passages.docid: 71479
negative_passages.text: Is there some elementary proof of invariance of domain?
negative_passages.docid: 62951
negative_passages.text: Is there a more direct way of proving that this ring is an integral domain?
negative_passages.docid: 141659
negative_passages.text: Every field is an integral domain
negative_passages.docid: 19178
negative_passages.text: $f$ continuous, $f^N$ analytic on a domain D implies $f$ analytic on D
negative_passages.docid: 89271
negative_passages.text: If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
negative_passages.docid: 141410
negative_passages.text: Injective integral domains are fields
negative_passages.docid: 106091
negative_passages.text: Showing $\mathcal{P}(X)$ is isomorphic to $2^X$
negative_passages.docid: 11259
negative_passages.text: Prove $R\times S$ is not an integral domain
negative_passages.docid: 115781
negative_passages.text: Proof about Holomorphic functions in the unit disc