If φ is onto and R' is a field, prove that Ker φ is a maximal ideal of R.
97605
Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
157876
If every prime ideal is maximal, what can we say about the ring?
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.
67237
Pull back image of maximal ideal under surjective ring homomorphism is maximal
124151
Finite ring extension and number of maximal ideals
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
67203
Complement of maximal multiplicative set is a prime ideal
44065
If $B$ is finitely generated as a $k$-algebra, and $\phi:A\to B$ is a $k$-algebra map, is $\phi^{-1}(M)$ maximal for any maximal $M\subset B$?
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
114640
Showing that an ideal is not a free $R-$module.
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
52966
Rings, ideals and units-proof
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
16643
A slick proof that a field which is finitely generated as a ring is finite
138752
Prove the Radical of an Ideal is an Ideal