Quotients of partial abelian monoids and the Riesz decomposition property

Abstract.

Partial abelian monoids (PAMs) are structures ($P; \bot, \oplus, 0$), where $\oplus$ is a partially defined binary operation with domain $\bot$, 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.