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New operations on partial abelian monoids defined by preideals. (English) Zbl 1154.81305
Summary: We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation \(\oplus\), which is given by restriction of the original partial operation \(+\) with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples.
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
08A55 Partial algebras
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