On lattice ordered groups having a unique addition
Ján Jakubík · Czechoslovak Mathematical Journal · 1990
Lattice ordered groups with unique addition (for definitions, cf.below) were investigated by P. Conrad and M. Darnel [1].The case oflinear ordered groups having this property was dealt with by T. Ohkuma [2].In [l] the following open question was proposed: (*) If G is a lattice ordered group such that the positive cone has a unique addition, then does G have a unique addition as well?It was remarked in [l] that the answer is yes if G is a Hnearly ordered group.In the present paper it will be shown that the answer is positive also in the general case.