Cancellative commutative semigroups

The study of t.c.r. (=totally cancellative reduced) real semigroups (which are just convex cones in real vector spaces, with the induced addition) enables us to answer some questions about t.c.r. semigroups in general. For example, a finite-dimensional divisible commutative semigroups is locally free if and only if it is t.c.r. and has the Riesz Interpolation Property. An address delivered at the Symposium on Semigroups and the multiplicative Structure of Rings in Mayagüez, 1970