The freeness of a group based on a distributive lattice
Paul Hill, H. Subramanian · Proceedings of the American Mathematical Society · 1975
Let L L be a distributive lattice and G G the abelian group with the following presentation. The generators of G G are the elements of the lattice L L , and the relations are ( a ∨ b ) + ( a ∧ b ) = a + b (a \vee b) + (a \wedge b) = a + b where a a and b b are arbitrary elements of L L . It is shown that G G is free abelian. In particular, G G is torsion free. The latter statement answers affirmatively a question posed several years ago by E. Weinberg.