Popis: |
We show that: (1) If ( G 1 , O 1 ) is a finitely generated divisibility group that is not lattice ordered and if ( G 2 , O 2 ) is a divisibility group such that Card ( G 2 ) > Card ( R ) , then the product ( G 1 , O 1 ) × ( G 2 , O 2 ) is not a divisibility group. (2) If ( G 1 , O 1 ) is a torsion free finitely generated divisibility group and if ( G 2 , O 2 ) is a lattice ordered group with only finitely many ultra filters, then the product ( G 1 , O 1 ) × ( G 2 , O 2 ) is a divisibility group if and only if Card ( G 2 ) ⩽ Card ( R ) . (3) If ( G 1 , O 1 ) and ( G 2 , O 2 ) are both torsion free finitely generated divisibility groups, then the product ( G 1 , O 1 ) × ( G 2 , O 2 ) is a divisibility group. |