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 $M\subset B$?
49521
In an extension of finitely generated $k$-algebras the contraction of a maximal ideal is also maximal
139100
A question on the group algebra $k[G]$ of a finite abelian group
123891
There are finitely many maps on nonnegative integers satisfying $\phi(ab)=\phi(a)+\phi(b)$
37570
$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
67237
Pull back image of maximal ideal under surjective ring homomorphism is maximal
109080
Is the kernel of a map to a finitely presented module finitely generated?
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
116883
About ideals in a ring which is a $k$ vector space
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
46040
Preimage of maximal ideal is maximal (why is this answer wrong?)
70047
Is the ideal generated by irreducible element in principal ideal domain maximal?
128861
If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
43814
What does it mean when a set is said to be a "finitely generated vector space"?
102871
$\langle r\rangle$ maximal $\iff r$ irreducible
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?