## Sum of observables on MV-effect algebras.(English)Zbl 1398.06012

Summary: Using a one-to-one correspondence between observables and their spectral resolutions, we introduce the sum of any two bounded observables of a $$\sigma$$-MV-effect algebra. This sum is commutative, associative with neutral element. Under the Olson order of observables, the set of bounded observables is a partially ordered semigroup, and the set of sharp observables is even a Dedekind $$\sigma$$-complete $$\ell$$-group with strong unit.

### MSC:

 06D35 MV-algebras 03G12 Quantum logic
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### References:

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