Game properties of Boolean algebras
We deal with unbounded dually residuated lattices that generalize pseudo -algebras in such a way that every principal order-ideal is a pseudo -algebra. We describe the connections of these generalized pseudo -algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo -algebra by means of the positive cone of a suitable -group . We prove that the lattice of all (normal) ideals of and the lattice of all (normal) convex -subgroups of are isomorphic....
We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We prove that every prelattice generalized effect algebra is a union of generalized MV-effect algebras and...
In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained...