Concepts of measures on ring-like quantum logics

The concepts of Q-valued measures, observables and states are introduced for ring-like quantum logics providing a unified approach to the basic notions of axiomatic quantum mechanics. Consequences of the existence of certain Q-valued measures for the underlying ring-like structures are investigated and the dependence of Q-valued measures on certain algebraic properties of ring-like quantum logics is studied. Moreover, links to the lattice-theoretic model of quantum logics are established.