Generalizations of pseudo MV-algebras and generalized pseudo effect algebras |
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Authors: | Jan Kühr |
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Affiliation: | (1) Department of Algebra and Geometry, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic |
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Abstract: | We deal with unbounded dually residuated lattices that generalize pseudo MV-algebras in such a way that every principal order-ideal is a pseudo MV-algebra. We describe the connections of these generalized pseudo MV-algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo MV-algebra A by means of the positive cone of a suitable ℓ-group G A . We prove that the lattice of all (normal) ideals of A and the lattice of all (normal) convex ℓ-subgroups of G A are isomorphic. We also introduce the concept of Archimedeanness and show that every Archimedean generalized pseudo MV-algebra is commutative. Supported by the Research and Development Council of the Czech Govenrment via the project MSM6198959214. |
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Keywords: | pseudo MV-algebra DRℓ -monoid generalized pseudo effect algebra |
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