If $K[X]/I \cong K[X]/J$ with $I \subset J$ then $I=J$?
6896
If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
74730
Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
158590
Why is it that if $[L:K]$ is finite, then $[L:K]$ is algebraic?
115695
If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
152104
How do I prove that $ij = k?$
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
145507
Is $K[a,b]=K(a,b)$ for algebraic $a, b$?
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
65371
Does $2^X \cong 2^Y$ imply $X \cong Y$ without assuming the axiom of choice?
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
147564
Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
155228
$X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?