Proving every prime ideal is maximal in a finite dimensional ring over a field.
116883
About ideals in a ring which is a $k$ vector space
74558
Localization of ideals at all primes
30714
A question on ring homomorphisms and maximal ideals.
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
110022
Showing prime and maximal ideal
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
76661
Checking the maximality of a principal ideal in $R[x]$
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.
104782
Polynomial irreducible - maximal ideal
94819
Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
150206
Every finitely generated algebra over a field is a Jacobson ring
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
33245
Show that every ideal of the ring $\mathbb Z$ is principal
92519
ideal behind Maximal ideals are Prime ideals
151829
Why are maximal ideals prime?