Let R be a domain with 1. Show that if aR = bR, then au = b for some unit u ∈ R.
60223
Two principal ideals coincide if and only if their generators are associated
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
4196
A valid proof for the invariance of domain theorem?
151852
How to prove $A \subset B \iff A \cup B = B$
7011
Integral domain with fraction field equal to $\mathbb{R}$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
105164
If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
32772
Proving units in a ring
6100
Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
89125
Prove that $r \in R$ such that $0 \lt r \lt 1$ then $\frac{1}{r (1 - r)} \ge 4$
5729
If $a^2+b^2+c^2=1$ then prove the following.
91786
Proving and disproving $\exists b,c\in \mathbb R$ such that $f(x)=\frac a2x^2+bx+c $
19909
if $abc=1$, then $a^2+b^2+c^2\ge a+b+c$