A Representation of Finite, Positive, Commutative Tomonoids
Thomas Vetterlein
We propose a representation of totally ordered monoids (or tomonoids, for short) that are commutative, positive, and finite. We identify these structures with compatible and positive total preorders on ℕn. To describe the latter, we utilise so-called direction f-cones, making use of the special form of the associated congruences on ℕn.