Lattice-ordered abelian groups finitely generated as semirings

Abstrakt

A lattice-ordered group (an L-group) can naturally be viewed as a semiring. We give a full classification of (abelian) L-groups which are finitely generated as semirings by first showing that each such L-group has an order-unit so that we can use the results of Busaniche, Cabrer and Mundici.

Then, we carefully analyze their construction in our setting to obtain the classification in terms of certain L-groups associated to rooted trees (Theorem 4.1)

Klíčová slova

• lattice-ordered
• abelian
• groups
• finitely
• generated
• semirings