Finitely Valued f-Modules, An Addendum

In an -group M with an appropriate operator set it is shown that the -value set (M) can be embedded in the value set (M). This embedding is an isomorphism if and only if each convex -subgroup is an -subgroup. If (M) has a.c.c. and M is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets ₁ and ₂ and the corresponding -value sets and . If R is a unital -ring, then each unital -module over R is an f-module and has exactly when R is an f-ring in which 1 is a strong order unit.