Question

How is $E = S(x)$, where $E = k(x), k$ a field, and S= k(I) of all rationals functions of $I = I(x) = \frac{(x^2 -x+1)^3}{x^2(x-1)^2}$?

score 37 · Answer 1 · 2019-06-29 13:52:30

How is $E = S(x)$, where $E = k(x), k$ a field, and S= k(I) of all rationals functions of $I = I(x) = \frac{(x^2 -x+1)^3}{x^2(x-1)^2}$?

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List Question

How is $E = S(x)$, where $E = k(x), k$ a field, and S= k(I) of all rationals functions of $I = I(x) = \frac{(x^2 -x+1)^3}{x^2(x-1)^2}$?

Some confusion about Gaussian ring

Amann/Escher, Analysis I, Exercise I.11.8: field automorphisms of $\mathbb{C}$ which leave the elements of $\mathbb{R}$ fixed

$p$-adic integers and valuation

Dedekind zeta function of a real quadratic field

Number fields with only trivial field automorphism

Minimal polynomial over a field extension

prove that $[F(\alpha):F]=p$ where $\alpha$ is a root of $x^p-a$

The splitting field of $x^p-1 \in \mathbb{Q}[x] $ where p is odd prime, contains a unique subfield of index 2

$K[X]=K(X)$ with X set of algebraic elements

Is there a finite field extension with „less“ intermediate fields than Aut-Subgroups?

Show that if Y is transcendental over a field K, and F is a field with $K\subset F\subset K(Y)$ and $K\neq F$ then Y is algebraic on F

Containment of $\mathbb Q(a)$

Is the subextension of a cyclotomic extension Galois?

Prime Factors of a Primitive Element

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