On lexico extensions of lattice ordered groups
Ján Jakubík · Czech digital mathematics library · 1983
JAN JAKUBlKThis note was inspired by Conrad's paper [1], namely by the main theorem of the paper, concerning the structure of lattice ordered groups G having the property that each orthogonal subset of G is finite.(Cf.Theorem (A) below.)While the 'if part of this theorem is obvious, by proving the 'only if part several non-trivial steps and auxiliary results were used (cf.also Conrad [3] and Fuchs [4]).By searching for a more simple and self-contained version of the proof of the 'only if part of this theorem it turned out that for obtaining a good basis enabling one to perform some rather simple induction steps we have at first to generalize the theorem under consideration.The case of lattice ordered groups G such that each upper-bounded orthogonal subset of G is finite (cf.[2]) will not be investigated in the present note.