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Quotients of partial abelian monoids and the Riesz decomposition property. (English) Zbl 1063.06011
Partial abelian monoids are structures \((P;\perp ,\oplus ,0)\) where \(\oplus \) is a partially defined binary operation with domain \(\perp \) which is commutative and associative in a restricted sense, and \(0\) is the neutral element. In the paper, partial abelian monoids with the Riesz decomposition property are studied. Relations with abelian groups, dimension equivalence and \(K_0\) for \(AF\;C^*\)-algebras are discussed.

MSC:
06F05 Ordered semigroups and monoids
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
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