Vol. 41, No. 3, 1972

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Tensor products of partially ordered groups

Jorge Martinez

Vol. 41 (1972), No. 3, 771–789

All groups considered in this paper are abelian. It is concerned for the most part with defining suitable tensor products on categories of partially ordered groups. There is introduced the purely auxiliary notion of a partial vector space for the purpose of leading to a reasonable construction of a “vector lattice cover”. The so-called o-tensor product from the category of p.o. groups into the category of lattice-ordered groups (l-groups) yields some surprising and surely disappointing results, such as that the functor G 0(.) preserves monics if and only if G is trivially ordered. This follows from the fact that if G is trivially ordered then G 0H is independent of the order on H and in fact l-isomorphic to the free l-group on the ordinary tensor product G H. It should be observed that the latter applies to torsion free groups only.

Mathematical Subject Classification
Primary: 06A55
Received: 4 December 1970
Revised: 8 January 1972
Published: 1 June 1972
Jorge Martinez