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Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

Jan Kühr (2008)

Czechoslovak Mathematical Journal

We deal with unbounded dually residuated lattices that generalize pseudo M V -algebras in such a way that every principal order-ideal is a pseudo M V -algebra. We describe the connections of these generalized pseudo M V -algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo M V -algebra A by means of the positive cone of a suitable -group G A . We prove that the lattice of all (normal) ideals of A and the lattice of all (normal) convex -subgroups of G A are isomorphic....

Generalized homogeneous, prelattice and MV-effect algebras

Zdena Riečanová, Ivica Marinová (2005)

Kybernetika

We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra P 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 P is a union of generalized MV-effect algebras and...

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