Timeline for Lattice-ordered group of rational rank 1
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2013 at 2:41 | comment | added | Todd Trimble | Certainly there are many partial orders on $\mathbb{Q}$ compatible with the group structure; all you need is a submonoid $P \subseteq \mathbb{Q}$ with the property that $x \in P$ and $-x \in P$ implies $x = 0$. For example, $P = \mathbb{N}$ would work: define $x \leq y$ to mean there is a nonnegative integer $n$ such that $y = n + x$. "Torsion free" refers only to group structure, not order structure; $\mathbb{Q}$ is of course torsion free. | |
| Jan 14, 2013 at 2:30 | comment | added | Rajnish | Is there ordered structure on the group of rational numbers $\mathbb Q$ which is not totally ordered? If the answer is yes, is that torsion free or not? | |
| Jan 14, 2013 at 0:29 | history | edited | Todd Trimble | CC BY-SA 3.0 |
added 813 characters in body
|
| Jan 13, 2013 at 23:04 | comment | added | Rajnish | @Trimble, thank you for the nice idea. | |
| Jan 13, 2013 at 22:54 | vote | accept | Rajnish | ||
| Jan 13, 2013 at 16:26 | history | answered | Todd Trimble | CC BY-SA 3.0 |