We describe a simple scheme for constructing finitely generated monoids in
which left-divisibility is a linear ordering and for practically investigating
these monoids. The approach is based on subword reversing, a general method of
combinatorial group theory, and connected with Garside theory, here in a
non-Noetherian context. As an application we describe several families of
ordered groups whose space of left-invariant orderings has an isolated point,
including torus knot groups and some of their amalgamated products.Comment: updated version with new result
