Directed colimits of free commutative semigroups
The main results of the paper were announced by the author earlier [Semigroup Forum 1, 162--168 (1970; Zbl 0211.33701); ibid. 1, 249--253 (1970; Zbl 0211.33702)]. He proves that a commutative monoid is a directed colimit of free commutative monoids iff It is cancellative, reduced, and has the strong Riesz interpolation property. A commutative semigroup without identity element is a directed colimit of free semigroups iff \(S\) with identity adjoined is a directed colimit of free monoids. If \(S\) is a cancellative, power-cancellative reduced commutative monoid, then it can be embedded into a directed colimit \(\bar{S}\) of free commutative monoids, so that every homomorphism of \(S\) into a directed colimit of free commutative monoids extends to \(\bar{S}\).
scientific article; zbMATH DE number 3558105