An embedding theorem with amalgamation for cancellative semigroups
John M Howie · Proceedings of the Glasgow Mathematical Association · 1963
Let {Si; i ε I} be a finite or infinite family of cancellative semigroups. Let U be a cancellative semigroup, and suppose that there exists, for each i in I, a monomorphism φi: u→ Si. We are interested in finding a semigroup T with the following properties. (a) For each i in I, there is a monomorphism λi: Si → T such that uφiλi = uøjλi for all u ɛ U and all i, j in I. That is to say, there exists a monomorphism λ: U → T which equals øiλi for all i in I. Siλi∩Sjλj = Uλ (i, j ε I; i ≠ j).