Deductive systems of a cone algebra — II: Isomorphism theorem |
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Authors: | N V Subrahmanyam |
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Institution: | (1) C/o Mr. N. Sapta Girisa, Aricent Cisco ODC, 4th Floor, Tower-B Presidency Building, Sector-14 Gurgaon, Haryana, 122 001, India |
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Abstract: | We prove that there is an isomorphism φ of the lattice of deductive systems of a cone algebra onto the lattice of convex ℓ-subgroups of a lattice ordered group (determined
by the cone algebra) such that for any deductive system A of the cone algebra, A is respectively a prime, normal or polar if and only if φ(A) is a prime convex ℓ-subgroup, ℓ-ideal or polar subgroup of the ℓ-group, thus generalizing and extending the result of Rachůnek
that the lattice of ideals of a pseudo MV-algebra is isomorphic to the lattice of convex ℓ-subgroups of a unital lattice ordered
group.
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Keywords: | cone algebra semi-ℓ g-cone pseudo MV-algebra deductive system ℓ -group ideal |
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