query: $|\bar{F}:F|=\infty$ implies that the degree of the irreducible polynomials in $F[x]$ is unbounded?
positive_passages.docid: 28658
positive_passages.text: $R$ with an upper bound for degrees of irreducibles in $R[x]$
negative_passages.docid: 7567
negative_passages.text: Degree of Field Extensions and $F(\alpha)$
negative_passages.docid: 127796
negative_passages.text: Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
negative_passages.docid: 5295
negative_passages.text: Can the graph of a bounded function ever have an unbounded derivative?
negative_passages.docid: 27675
negative_passages.text: Polynomials vanishing on an infinite set
negative_passages.docid: 132572
negative_passages.text: Why this polynomial is irreducible?
negative_passages.docid: 107842
negative_passages.text: Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
negative_passages.docid: 41693
negative_passages.text: Use irreducible fibers to show $X$ is irreducible
negative_passages.docid: 121217
negative_passages.text: How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$?
negative_passages.docid: 4192
negative_passages.text: Non-algebraically closed field in which every polynomial of degree $<n$ has a root
negative_passages.docid: 27577
negative_passages.text: An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
negative_passages.docid: 41173
negative_passages.text: If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
negative_passages.docid: 154360
negative_passages.text: Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
negative_passages.docid: 156727
negative_passages.text: A step in the proof of Characterization of $W^{1,\infty}$
negative_passages.docid: 49781
negative_passages.text: Existence of the absolute value of the limit implies that either $f \ $ or $\bar{f} \ $ is complex-differentiable
negative_passages.docid: 82229
negative_passages.text: Show if complex function $f(z)$ contains all real coefficients then $f(\bar z)$ = $\bar {f(z)}$
negative_passages.docid: 128658
negative_passages.text: Analyticity of $\overline {f(\bar z)}$ given $f(z)$ is analytic