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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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