If $[E:F] = p$, with $p$ a prime. There are no intermediate fields between $E$ and $F$
137715
If $[L:K]$ is prime, show that $L/K$ is a simple extension.
135152
Non-UFD integral domain such that prime is equivalent to irreducible?
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
153869
Under what $p$, $-1$ is a square in $\mathbf F_p$?
140497
Irreducibles are prime in a UFD
24988
Prove there exists $m > 2010$ such that $f(m)$ is not prime
14270
Polynomial divisibility is unchanged by coeff. field extension
70776
Characteristic of a field is $0$ or prime
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
41173
If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
48405
Why does the characteristic of a finite field always have to be prime?
68221
Question regardles primes and the fundamental theorem of arithmetic
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$