Characteristic of a field $F$ is prime
70776
Characteristic of a field is $0$ or prime
112045
A property of minimal prime ideal
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
122952
Degree of extension is equal to linear combination of prime factor multiplicities with prime factor index coefficients in Dedekind domains
93632
Existence of a ring homomorphism implies characteristic divisibility
59882
is it possible for two fields with the same characteristic to not be isomorphic?
57084
Characteristic of the following field?
68065
Quadratic extensions in characteristic $2$
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
147200
Given fields $K\subseteq L$, why does $f,g$ relatively prime in $K[x]$ imply relatively prime in $L[x]$?
98540
If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
135586
Prove that the preimage of a prime ideal is also prime.
146304
prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
37929
Classification of prime ideals of $\mathbb{Z}[X]$