We show that a lattice-ordered field (not necessarily commutative) is totally ordered if and only if each square is positive, answering a generalized question of Conrad and Dauns [6] in the affirmative. As a consequence, any lattice-ordered skew-field in [5] is totally ordered. Furthermore , we note that each lattice order determined by a pre-positive cone P on a skew-filed F is linearly ordere...

Abstract First we give a necessary and sufficient condition for an abelian lattice ordered group to admit expansion Riesz space (or vector lattice). Then construct totally with two non-isomorphic structures, thus improving previous paper where the example was non-totally group. This answers question raised by Conrad in 1975. We also partial solution another problem considered same paper. Finall...