This paper, entitled (appropriately enough) "Discrete Ordered Rings", might be of some help.

In particular, look at Theorem 11.1 on page 135. It states that if

*R* is an ordered ring with unity and if

*a* is an element of

*R*, then the order in

*R* extends to the ring of polynomials

.

**Moreover, if ***R* is discrete, then so is *S*. (The proof follows in the paper, and explains how the ordering works.)

So, given that the integers give you a discrete ordered ring, it seems as though you could just pick your favorite integer (I like 8) and then form the polynomial ring

, and that would then be yet another example of a discrete ordered ring by the above theorem.

Hopefully I have understood this correctly, and this helps you out!