Embedding actions of cancellative directed semigroups (Q5936173)

If \(S\) is a semigroup and \(X\) a set, then a right semigroup action is a mapping \(X\times S\to X\): \((x,s)\mapsto x\bullet s\) satisfying \((x\bullet s)\bullet t=x\bullet(st)\) for all \(x\in X\) and \(s,t\in S\). The author generalizes Ore's theorem about embeddability of semigroups into groups obtaining embeddings of semigroup actions into group actions. He considers an interpretation via direct limits.