Prove that $a=b$, where $a$ and $b$ are elements of the integral domain $D$
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
120292
How to formally prove: if $d\mid da+b$, then $d\mid b$?
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
112345
In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
126503
Showing that an integral domain is a PID if it satisfies two conditions
81794
Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$
62951
Is there a more direct way of proving that this ring is an integral domain?
61868
Prove that $ND = DN$ where $D$ is a diagonalizable and $N$ is a nilpotent matrix.
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
33645
Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$.
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$