# Deductive systems of a cone algebra (Part 2): Isomorphism theorem

In: Mathematica Slovaca, vol. 58, no. 6
N. V. Subrahmanyam

## Details:

Year, pages: 2008, 671 - 684
We prove that there is an isomorphism $φ$ of the lattice of deductive systems of a cone algebra onto the lattice of convex $\ell$-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 $\ell$-subgroup, $\ell$-ideal or polar subgroup of the $\ell$-group, thus generalizing and extending the result of Rach\r{u}nek that the lattice of ideals of a pseudo MV-algebra is isomorphic to the lattice of convex $\ell$-subgroups of a unital lattice ordered group.