If $K$ is a field, prove the polynomial ring $K[x]$ has infinitely many maximal ideals.
94174
Ring of polynomials over a field has infinitely many primes
129371
Maximal ideals in the ring of real functions on $[0,1]$
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
116883
About ideals in a ring which is a $k$ vector space
138572
Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
144245
Shorter proof of $R/I$ is a field if and only if $I$ is maximal
133975
Localising a polynomial ring and non-maximal prime ideal
103948
Minimal polynomial is invariant under field extensions
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
74537
Maximal Ideals in $K[y]$
154487
Maximal number of monomials of multivariate polynomial
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
89782
To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field
74150
Problem on the number of generators of some ideals in $k[x,y,z]$
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number