If $A$ is a semilocal ring and $f : A \twoheadrightarrow B$, then $f(\text{rad}(A)) = \text{rad}(B)$?
103491
If $A$ is a semilocal ring and $f:A\rightarrow B$ is a surjective homomorphism, then $f(\operatorname{rad}A)=\operatorname{rad}B$
30714
A question on ring homomorphisms and maximal ideals.
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
119067
Basic Ring Theory Question involving the unit element
110661
When does $\sqrt{a b} = \sqrt{a} \sqrt{b}$?
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
42871
Quotient of a local regular ring
69649
If an ideal contains the multiplicative identity, then it is the whole ring
76674
Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
29359
Localisation isomorphic to a quotient of polynomial ring
39576
Quotient ring being isomorphic to the initial ring
84206
How do I show that if $f$ is entire and $\{\lvert f(z)\rvert < M\}$ is connected for all $M$, then $f$ is a power function?
98818
Quotient ring of a localization of a ring
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
38963
Ideals in ring of continuous functions $\mathcal{C}[0,1]$ ... NBHM- Algebra