Tensor products of structures with interpolation
While it is known that tensor products of dimension groups are dimension groups, the corresponding problem for interpolation groups has been open for a while. In this paper, this problem is solved (negatively), by finding two torsion-free Riesz groups whose tensor product (in the category of partially ordered abelian groups) does not satisfy interpolation. The Riesz groups of this example are obtained by lexicographical product of the rationals by finitely presented, non directed partially ordered abelian groups. Analogous problems for refinement monoids (in the category of commutative monoids) or lattice-ordered abelian groups (in the category of partially ordered abelian groups) are also solved.
category of partially ordered abelian groups
scientific article; zbMATH DE number 950236