Partial residuated structures and quantum structures (Q939179)

The authors generalize the notion of an adjoint pair on a poset to the notion of a partial adjoint pair. They study properties of partial adjoint pairs and introduce the so-called partial residuated lattice. It is shown that a lattice effect algebra forms a partial residuated lattice and a characterization of partial residuated lattices forming lattice effect algebras is given. Some results in the non-commutative case are presented.