I am looking for concrete examples of cancellative, left reversible semigroups. Left reversible semigroups are also called "Ore semigroups". See [this wikipedia page](http://en.wikipedia.org/wiki/Special_classes_of_semigroups) for the definition of a left reversible semigroup. Of course, commutative semigroups are automatically left reversible, and I am looking for non-commutative examples.


Please also mention if these semigroups arise in an interesting setting. 



Examples of left reversible semigroups
Some examples and further references (and an interesting setting) are given in this paper by Laca:


<http://arxiv.org/abs/math/9911135>


See section 1.1, pages 2-3.


