0
$\begingroup$

I have a question about ordered integral domains. What do I need to do to prove that for $a \in D^p$, $-a \in D^p$, or $a = 0$ and $b \in D^p$, $-b \in D^p$ or $b = 0$ then

1) $\mathrm{abs}(a) \geq a \geq -\mathrm{abs}(a)$

and

2) $\mathrm{abs}(a) + \mathrm{abs}(b) \geq \mathrm{abs}(a+b)$.

Do I need to split each equation by switching the inequality sign?

  • 0
    Is $D^p$ meant to be the positive class? It's usually denoted $D_+$ or $D^+$, not $D^p$ (which might be confused with the set of $p$th powers in $D$).2011-04-20

2 Answers 2