Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.
An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.
We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation ⊕, which is given by restriction of the original partial operation + with respect to a special subset called . We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples.