Let $\phi: R \to S$ be a homomorphism of rings, $I$ an ideal of $R$, $J$ an ideal of $S$.
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
27670
Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
73235
Rings $R/I \cong h(R)/h(I)\,$ for injective ring hom $h$
64048
Describe all ring homomorphisms
157378
On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
37393
$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
60760
Ring homomorphism and characteristic
131946
Order of an Element Under a Homomorphism
29019
Ideals in direct product of rings
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
111307
If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
129858
"Almost" ring homomorphism
11573
Rings and some of their properties
30714
A question on ring homomorphisms and maximal ideals.
144928
Find all primes $p$ such that $\phi(x)=x^{13}$ is a homomorphism $\Bbb Z/p\Bbb Z \rightarrow \Bbb Z/p\Bbb Z$.
122958
$R/I$ is commutative iff $rs-sr \in I$