Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can we define a compatible ordering in $\Bbb{Z}_m$?

The ordering is compatible with the operation if:

$x,y,z \in G$ with $x\leq y$ then $x\cdot z\leq y\cdot z$

I have the belief that we can not find this ordering, but how can I prove it?

share|improve this question

2 Answers 2

Hint: Consider whether $x<e$ or $x>e$ for arbitrary $x$; where $e$ is the identity element.

share|improve this answer
    
Thank you for your help. –  art Mar 30 '13 at 16:50

In case you ask about $(\mathbb{Z}/m,+)$: Try to prove that ordered groups are trivial or infinite.

share|improve this answer
    
It appears that OP is interested in the multiplicative monoid of $\Bbb{Z}_{m}$, where $m$ looks arbitrary. –  Andreas Caranti Mar 23 '13 at 18:21

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.