Affiliation:
1. Pokroku 5 SK-040 11 Košice Slovakia
Abstract
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.
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