Partial abelian monoids (PAMs) are structures $(P,\oplus, 0)$, where
$\oplus$ is a partially defined binary operation which is
commutative and associative in a restricted sense, and $0$ is the
neutral element. PAMs with the Riesz decomposition properties and
binary relations with special properties on PAMs are studied.
Relations with abelian groups,  dimension equivalence  and $K_0$ for
AF C*-algebras are discussed.
