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.