Deductive systems of a cone algebra — II: Isomorphism theorem

摘要

We prove that there is an isomorphism ?? of the lattice of deductive systems of a cone algebra onto the lattice of convex a?“-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 ??(A) is a prime convex a?“-subgroup, a?“-ideal or polar subgroup of the a?“-group, thus generalizing and extending the result of Rach?ˉnek that the lattice of ideals of a pseudo MV-algebra is isomorphic to the lattice of convex a?“-subgroups of a unital lattice ordered group.