Generalizations of Boolean algebras. An attribute exploration
Generalizations of pseudo MV-algebras and generalized pseudo effect 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....
Generalized homogeneous, prelattice and MV-effect algebras
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...
Generalized join-hemimorphisms on Boolean algebras.
Generalized Post algebras and their application to some infinitary many-valued logics [Book]
GMV-algebras and meet-semilattices with sectionally antitone permutations