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ON THE STRUCTURE OF LATTICE ORDERED GROUPS
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a,beP Archimedean classes Archimedean group Boolean algebra carriers of G classes of G closed convex subsemigroups commutative compl Consequently Corollary denoted directed subgroup distributive lattice element aeG element of G equivalence relation full group fully ordered group function lattice G is relatively group G group homomorphism Hence homomorphism cp homomorphism with kernel implies Intr join homomorphism l.group G lattice and group lattice homomorphism lattice of Archimedean lattice of carriers lattice of X0-classes lattice ordered group lattice ordered vector Lemma Let G mapping maximal element medean classes meet homomorphism minimal element ordered vector group partially ordered set pointwise ordering positive cone positive elements preorder Proof pseudo strong units real valued functions relatively complemented lattice resp Riesz space set of elements simple functions solid subgroup subgroup of G Theorem 1.3 tralie upperbound vector lattice weak units X0-classes of G X0-klassen