Lexico groups and direct products of lattice ordered groups
Ján Jakubík · Mathematica Slovaca · 2016
Abstract A lattice ordered group A will be said to be a lexico group if there exists a convex ℓ-subgroup A 0 of A with A 0 ≠ A such that for each a ∈ A\A 0 we have either a > a 0 for each a 0 ∈ A 0, or a < a 0 for each a 0 ∈ A 0. We prove the following result. Let A be a convex ℓ-subgroup of a lattice ordered group ∈ such that (i) A is a lexico group, and (ii) A fails to be upper bounded in G. Then A is a direct factor of G.